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tan4x+tan2x=sec4x−sec2xtan^4x+tan^2x=sec^4x-sec^2x

Step-by-step Solution

Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity tan(x)^4+tan(x)^2=sec(x)^4-sec(x)^2. Starting from the right-hand side (RHS) of the identity. Factor the polynomial \sec\left(x\right)^4-\sec\left(x\right)^2 by it's greatest common factor (GCF): \sec\left(x\right)^2. Apply the trigonometric identity: \sec\left(\theta \right)^2-1=\tan\left(\theta \right)^2. Applying the trigonometric identity: \sec\left(\theta \right)^2 = 1+\tan\left(\theta \right)^2.
Prove the trigonometric identity tan(x)^4+tan(x)^2=sec(x)^4-sec(x)^2

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Final answer to the exercise

true

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Similar Questions Solved

11−sin(x)−11+sin⁡(x)=2tan⁡(x)sec(x)\frac{1}{1-sin\left(x\right)}-\frac{1}{1+\sin\left(x\right)}=2\tan\left(x\right)sec\left(x\right)

tan(x)+cot(x)=sec(x)cosec(x)tan\left(x\right)+cot\left(x\right)=sec\left(x\right)cosec\left(x\right)

1+cos⁡2xsin⁡2x=cot⁡x\frac{1+\cos2x}{\sin2x}=\cot x

sec(x)−tan(x)sin(x)=1sec(x)sec\left(x\right)-tan\left(x\right)sin\left(x\right)=\frac{1}{sec\left(x\right)}

tan⁡(x)+cot⁡(x)=sec⁡(x)csc⁡(x)\tan\left(x\right)+\cot\left(x\right)=\sec\left(x\right)\csc\left(x\right)

tan⁡(a)+cot⁡(a)=sec⁡(a)csc⁡(a)\tan\left(a\right)+\cot\left(a\right)=\sec\left(a\right)\csc\left(a\right)

sec⁡x−sin⁡xtan⁡x=cos⁡x\sec x-\sin x\tan x=\cos x

Main Topic: Proving Trigonometric Identities

To prove a trigonometric identity, you have to show that one side of the equation can be transformed into the other side.

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tan4x+tan2x=sec4x−sec2x
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