Question

Prove the identity. tan(2x) = (2 sin(x) cos(x)) / (2 cos^2(x) - 1) Recall the double angle formulas for sine and cosine. (2 sin(x) cos(x)) / (2 cos^2(x) - 1) = sin( [ ] ) / (2 cos^2(x) - 1) = sin(2x) / cos( [ ] ) = [ ]

          Prove the identity.
tan(2x) = (2 sin(x) cos(x)) / (2 cos^2(x) - 1)
Recall the double angle formulas for sine and cosine.
(2 sin(x) cos(x)) / (2 cos^2(x) - 1) = sin( [ ] ) / (2 cos^2(x) - 1)
= sin(2x) / cos( [ ] )
= [ ]

Added by Donald C.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Piyush Kumar Gupta

03/27/2022

Step 1

Step 1: Start with the right-hand side of the identity we want to prove: \( \frac{2\sin(x)\cos(x)}{\cos^2(x) - 1} \). Show more…

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Prove the identity: tan(2x) = 2sin(x)cos(x) / (cos^2(x) - 1) Recall the double angle formulas for sine and cosine: 2sin(x)cos(x) = sin(2x) cos^2(x) - 1 = -cos^2(x) + 1 = -cos(2x)