Using the chain rule, we have that \ \frac{d}{dx}\tan^3 x = 3 \tan^2 x \times \frac{d}{dx}\tan x= 3\tan^2 x \sec^2x · Divide both side by cos^2x and we get sin^2x/cos^2x cos^2x/cos^2x = 1/cos^2x tan^2x 1 = sec^2x tan^2x = sec^2x 1 Confirming that the result is an identityDifferentiate c and d, use the product rule to find v The easiest way to integrate tanx power n is to have sec^2x as it is the differentiation of tanx All u need to know is chain rule 0
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Differentiate 2 tan x sec^2x- · Ie for the second derivative of sec^2x d/dx 2 sec^2x ( tan x ) but you could also note that sec^2 x = 1 tan^2 x, and I'm sure you can differentiate tan^2 x with the chain rule 0 f1mad Badges 13 Rep? · Hint consider whole sec2(x)tan(x) = v as its integral then apply by parts to get x2tan2(x) − (∫ 4xtan2(x)) again consider tan2(x) as v and apply by parts Note use tan2(x) = sec2(x) − 1 and proceed with the integration join both these parts to get the integral share Share a link to this answer Copy link
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#15 Report 9 years ago #15 Quotient rule 1/cos^2xX and y are independent variables, d is the differential operator, int is the integration operator, C is the constant of integration Identities tan x = sin x/cos x equation 1 cot x = cos x/sin x equation 2 sec x = 1/cos x equation 3 csc x = 1/sin x equation 4 cot x = 1/tan x equation 5 sin 2 x cos 2 x = 1 equation 6 tan 2 x 1An alternative method is to take `sec^2 x ` and replace it by `1/(cos^2 x)` Replace `1/(cos^2 x)` by `1 tan^2 x` (the basic formula of trigonometry `1tan^2 x = 1/(cos^2 x)` )
· Get an answer for 'How do you prove the identity `(tanxcotx)^2=sec^2x csc^2x ?` ``' and find homework help for other Math questions at eNotesClick here👆to get an answer to your question ️ Prove sec^4x sec^2x = tan^4x tan^2xAbout Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How works Test new features Press Copyright Contact us Creators
Get answer sec^1((1tan ^2x),(1tan ^2 x)) Apne doubts clear karein ab Whatsapp par bhi Try it nowSolve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and moreIntegral tan^2(x)sec(x)powers of secant and tangent Integral tan^2(x)sec(x)powers of secant and tangent
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Antiderivative of 2tan x sec x Compute tan x sec 2 x dx in two different ways a) By substituting u = tan x b) By substituting v = sec x c) Compare the two results Solution a) Compute tan x sec 2 x dx by substituting u = tan x If u = tan x 2then du = sec x dx and tan x sec 2 x dx = u du = 1 u2 c 2 = 1 tan2 xSimplify (sec(x)^2)/(tan(x)) Separate fractions Rewrite in terms of sines and cosines Multiply by the reciprocal of the fraction to divide by Convert from to Divide by Rewrite in terms of sines and cosines Rewrite in terms of sines and cosines Apply the product rule to Multiply and Cancel the common factor of and`(sin^2 x cos^2 x)/(cos^2 x) = (sin^2 x cos^2)/(cos^2 x)` valid Hence, testing if the `tan^2 x 1= sec^2 x` holds yields that it is a valid statement Approved by eNotes Editorial Team
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Simplify (tan(x)^2)/(sec(x)^2) Rewrite as Rewrite in terms of sines and cosines Rewrite in terms of sines and cosines Multiply by the reciprocal of the fraction to divide by Write as a fraction with denominator Cancel the common factor of Tap for more steps Cancel the common factorEvaluate the given integral We do this knowing that a substitution would help us integrate this problem First, we apply the trigonometric identity of {eq}\displaystyle \sec^2 x = 1\tan^2 x {/eq}Let u=sec^2 and v=tan^2 and if that's still too much at this stage Let a=sec b=sec c=tan d=tan Differentiate a and b, use the product rule to find u;
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Solve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and moreProve sec^2(x) csc^2(x) = tan^2(x) cot^2(x)Solve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and more
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Solve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and moreCot (x) = cot (x) sin ^2 (x) cos ^2 (x) = 1 tan ^2 (x) 1 = sec ^2 (x) cot ^2 (x) 1 = csc ^2 (x) sin (x y) = sin x cos y cos x sin y cos (x y) = cos x cosy sin x sin y tan (x y) = (tan x tan y) / (1 tan x tan y) sin (2x) = 2 sin x cos x cos (2x) = cos ^2 (x) sin ^2 (x) = 2 cos ^2 (x) 1 = 1 2 sin ^2 (x) · If units of degrees are intended, the degree sign must be explicitly shown (eg, sin x°, cos x°, etc) Using this standard notation, the argument x for the trigonometric functions satisfies the relationship x = (180x/π)°, so that, for example, sin π = sin 180° when we take x = π In this way, the degree symbol can be regarded as a
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Calculus 2, integral of (1tan^2x)/sec^2x, integral of cos(2x)Sec(x)^22=tan(x)^2 Replace the with based on the identity Subtract from Move all terms containing to the left side of the equation Tap for more steps Subtract from both sides of the equation Simplify the left side of the equation Tap for more steps Rewrite as Factor out ofAs there is no way to immediately integrate tan^2(x) using well known trigonometric integrals and derivatives, it seems like a good idea would be writing tan^2(x) as sec^2(x) 1 Now, we can recognise sec^2(x) as the derivative of tan(x) (you can prove this using the quotient rule and the identity sin^2(x) cos^2(x) = 1), while we get x when we integrate 1, so our final answer is tan(x) x
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We know the identity sin 2 (x)cos 2 (x)=1 ——(i) Dividing throughout the equation by cos 2 (x) We get sin 2 (x)/cos 2 (x) cos 2 (x)/cos 2 (x) = 1/cos 2 (x) We know that sin 2 (x)/cos 2 (x)= tan 2 (x), and cos 2 (x)/cos 2 (x) = 1 So the equation (i) after substituting becomes tan 2 (x) 1= 1/cos 2 (x) ——–(ii) Now we know that 1/cos 2 (x)= sec 2 (x) So on substitutionAbout Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How works Test new features Press Copyright Contact us Creators$$ \tan^2x \sec^2x $$ since $\sec ^2x=1\tan ^2 x$ so $$\tan^2x (1\tan ^2x)\implies 1$$ Share Cite Follow answered Jun 5 '13 at 1025 iostream007 iostream007 4,239 3 3 gold badges 19 19 silver badges 40 40 bronze badges $\endgroup$ Add a comment Your Answer
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· `tan^2 x = 3 tan x` Solve for x 1 Educator answer Math Latest answer posted August 23, 14 at PM Solve the equation sec^2x 2 tan x = 4 1 Educator answer · tan2x = 1 3 tanx = ± √3 3 x = π 6 ± πn x = 5π 6 ± πn Where n is an element of all real numbers graph {2 (secx)^2 (tanx)^23 10, 10, 5, 5} Answer linkFree trigonometric equation calculator solve trigonometric equations stepbystep
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· (tan x)' = sec^2 x Let f(x) = tanx We know that tanx = sinx/ cosx ==> f(x) = sinx/ cosx Now to differenctiate f(x) we will use the chain rule f(x) = u/v such that u= sinx ==> u' = cosxTan(x)^22sec(x)=2 Replace the with based on the identity Reorder the polynomial Factor using the AC method Tap for more steps Consider the form Find a pair of integers whose product is and whose sum is In this case, whose product is and whose sum is · If you know the identity $\sec^2x=1\tan^2x$, then this easily simplifies to $$\sec^2 x\tan^2 x$$ $$=(1\tan^2x)\tan^2x$$ $$=1$$ But in your question you mentioned reciprocals, so I am assuming you can't use the above identity In that case, you can do the following
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· We can use the product and chain rules, and then simplify to find the derivative of 2sec 2 (x)tan(x) is 4sec 2 (x)tan 2 (x) 2sec 4 (x) The second derivative of sec^2x is 4sec 2 (x)tan 2 (x) 2sec 4 (x) Interesting property of the derivative of sec^2x It is interesting to note that the derivative of sec 2 (x) is equal to the derivative of tan 2 (x) · Ex 74, 9 sec 2 tan 2 4 Let tan = Diff both sides wrt x sec 2 = = sec 2 Integrating the function sec 2 tan 2 4 Putting value of tan = and = sec 2 = sec 2 t · The Second Derivative Of tan^2x To calculate the second derivative of a function, differentiate the first derivative From above, we found that the first derivative of tan^2x = 2tan(x)sec 2 (x) So to find the second derivative of tan^2x, we need to differentiate 2tan(x)sec 2 (x) We can use the product and chain rules, and then simplify to find the derivative of 2tan(x)sec 2 (x
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Solve for x sec(x)^22tan(x)=4 Replace the with based on the identity Reorder the polynomial Factor using the AC method Tap for more steps Consider the form Find a pair of integers whose product is and whose sum is In this case, whose product is and whose sum is
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