Question

I’m supposed to prove this identity but it’s not working for me

Answer 1

Given

`(cot\theta+tan\theta)^2=csc^2\theta+sec^2\theta`

Step-by-step explanation

From the left hand sie

`\begin{gathered} (cot\theta+tan\theta)^2=cot^2\theta+2cot\theta tan\theta+tan^2\theta \\ Next \\ since\text{ tan}^2\theta=sec^2\theta-1\text{ and }cot^2=csc^2\theta-1 \\ (cot\theta+tan\theta)^2=sec^2\theta-1+2cot\theta tan\theta+csc^2\theta-1 \\ (cot\theta+tan\theta)^2=sec^2\theta-1+2(cos\theta)/(sin\theta)*(sin\theta)/(cos\theta)+csc^2\theta-1 \\ (cot\theta+tan\theta)^2=sec^2\theta-1+2+csc\theta-1 \\ (cot\theta+tan\theta)^2=csc^2\theta+sec^2\theta \end{gathered}`