Question

Question #297ca

Answer 1

`cottheta`

Explanation:

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

`•color(white)(x)cottheta=costheta/sintheta`

`•color(white)(x)sectheta=1/costheta`

`rArrcot^2theta . sintheta .sectheta`

`=(cos^2theta)/(sin^2theta)xxsinthetaxx1/costheta`

`=(cancel(costheta)costheta)/(cancel(sintheta)sintheta)xxcancel(sintheta)xx1/cancel(costheta)`

`=costheta/sintheta`

`=cottheta`

`color(red)"OR"`

`costheta/sintheta=costhetaxx1/sintheta=costhetacsctheta`

Answer 2

`cot^2 theta * sintheta * sectheta = cot theta`

Explanation:

`cot^2 theta * sintheta * sectheta`

Rewrite in terms of `sin` and `cos`

`= (cos^2theta / sin^2theta) * sintheta * (1/costheta)`

`= frac{costheta * color(red)(costheta) * color(red)(sintheta)}{sintheta * color(red)(sintheta) * color(red)(costheta) }`

`= cottheta`