Question

How do you simplify `csc^2(theta) / (1 + tan^2(theta) )`?

Answer 1

`cot^2theta`

Explanation:

`"using the "color(blue)"trigonometric identities"`

`•color(white)(x)1+tan^2theta=sec^2theta`

`•color(white)(x)csctheta=1/sintheta" and "sectheta=1/costheta`

`=csc^2theta/sec^2theta`

`=(1/sin^2theta)/(1/cos^2theta)`

`=1/sin^2thetaxxcos^2theta=cos^2theta/sin^2theta=cot^2theta`