Question

Simplify 1- cos^2 Θ / cos^2 Θ Answers sin2 θ cos2 θ tan2 θ 1

Answer 1

$\\ \rm\Rrightarrow \dfrac{1-cos^2\theta}{cos^2\theta}$

$\\ \rm\Rrightarrow \dfrac{sin^2\theta}{cos^2\theta}$

$\\ \rm\Rrightarrow tan^2\theta$

Option C

Answer 2

Answer:

Trigonometric identities

$\large \begin{aligned}\cos^2 \theta + \sin^2 \theta & = 1\\\implies \quad \quad \sin^2 \theta & = 1 - \cos^2 \theta\\\\\tan \theta=\dfrac{\sin \theta}{\cos \theta} \end{aligned}$

Therefore, using the identities, the given expression can be simplified as follows:

$\large\begin{aligned}\implies \dfrac{1- \cos^2 \theta}{\cos^2 \theta} & = \dfrac{\sin^2 \theta}{\cos^2 \theta}\\\\& = \tan^2 \theta\end{aligned}$