Prove the trigonometry identitied. \frac{\sec A}{\sec A-1}-\frac{\sec A+1}{\tan^2A}=1

Harlen Pritchard

Harlen Pritchard

Answered question

2021-09-10

Prove the trigonometry identitied
secAsecA1secA+1tan2A=1

Answer & Explanation

faldduE

faldduE

Skilled2021-09-11Added 109 answers

Solve the LHS. Use the identity (a+b)(ab)=a2b2
LHS=secAsecA1secA+1tan2A
=secAtan2A(secA+1)(secA1)(secA1)tan2A
=secAtan2A(sec2A1)(secA1)tan2A
Use the identity sec2θ1=tan2θ.
LHS=secAtan2Atan2A(secA1)tan2A
=tan2A(secA1)(secA1)tan2A
=1
=RHS
Since LHS=RHS. Hence secAsecA1secA+1tan2A=1 proved.
Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?