Question

Which of the following is equivalent to meet for all values of 0 for which seat, is defined?

Answer 1

Given:

The trigonometric expression is,

`(\sec ^2\theta-1)/(\sec ^2\theta)`

Step-by-step explanation:

Simplify the expression.

`\begin{gathered} (\sec^2\theta-1)/(\sec^2\theta)=(\tan ^2\theta)/(\sec ^2\theta)\text{ \lbrack}sec^2\theta+tan^2\theta=1\text{\rbrack} \\ =(\sin^2\theta)/(\cos^2\theta)\cdot(1)/(\sec ^2\theta) \\ =(\sin^2\theta)/(\cos^2\theta)\cdot\cos ^2\theta \\ =\sin ^2\theta \end{gathered}`

So equivalent expression is,

`\sin ^2\theta`