Prove that trigonometric identity

Question

1/(cosx + sinx) +) 1/(cosx - sinx) = tan2xcscx

 

Answer 1

1/(cosx + sinx) + 1/(cosx - sinx)

=1/(cosx + sinx) + 1/(cosx - sinx)

=(cosx-sinx+cosx+sinx)/(cosx + sinx) (cosx - sinx)

=2cosx/(cos^2x-sin^2x)

=2cosx/cos2x

Multiply and divide with sinx

=2sinxcosx/cos2xsinx

=sin2x/cos2xsinx

=tan2xcscx