Question

(cot θ + tan θ) equals ______.

Options

• cosec θ sec θ

• sin θ sec θ 

• cos θ tan θ

• sin θ cos θ

Answer 1

(cot θ + tan θ) equals cosec θ sec θ.

Explanation:

`cot theta = 1/tantheta`

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

= `cos theta/sin theta`

∴ cot θ + tan θ

= `cos theta/sin theta + sin theta/costheta`

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

= `1/(sin theta cos theta)`     ...(∵ cos² θ + sin² θ = 1)

= `1/sin theta * 1/costheta`

= cosec θ sec θ