178k views
3 votes
I’m supposed to prove this identity but it’s not working for me

I’m supposed to prove this identity but it’s not working for me-example-1
User Dimatura
by
8.4k points

1 Answer

4 votes

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}

User MarsPeople
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories