Question

How do you verify the identity `1/(1-sintheta)+1/(1+sintheta)=2sec^2theta`?

Answer 1

See below.

Explanation:

`1/(1-sintheta)+1/(1+sintheta)=2sec^2theta`
`1/(1-sintheta)+1/(1+sintheta)=((1+sintheta)+(1-sintheta))/((1-sintheta)(1+sintheta))=2/(1-sin^2theta) = 2/cos^2theta = 2 sec^2theta`