Question

Simplify 1- cos^2 Θ / cos^2 Θ

Answers

sin2 θ

cos2 θ

tan2 θ

1

Answer 1

`\\ \rm\Rrightarrow (1-cos^2\theta)/(cos^2\theta)`

`\\ \rm\Rrightarrow (sin^2\theta)/(cos^2\theta)`

`\\ \rm\Rrightarrow tan^2\theta`

Option C

Answer 2

Trigonometric identities

`\large \begin{aligned}\cos^2 \theta + \sin^2 \theta & = 1\\\implies \quad \quad \sin^2 \theta & = 1 - \cos^2 \theta\\\\\tan \theta=(\sin \theta)/(\cos \theta) \end{aligned}`

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

`\large\begin{aligned}\implies (1- \cos^2 \theta)/(\cos^2 \theta) & = (\sin^2 \theta)/(\cos^2 \theta)\\\\& = \tan^2 \theta\end{aligned}`