## Related questions with answers

Question

Verify the identity by transforming the lefthand side into the right-hand side.

$\left(1-\sin ^2 \theta\right)\left(1+\tan ^2 \theta\right) = 1$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 2Simplify using the Pythagorean identities $\sin^2\theta+\cos^2\theta=1$ and $1+\tan^2\theta=\sec^2\theta$.

$\begin{aligned} \left(1-\sin^2\theta\right)\left(1+\tan^2\theta\right)&=1\\ \cos^2\theta\cdot\sec^2\theta&=1 \end{aligned}$

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