Prove:

1/cos2A+sin2A/cos2A=sinA+cosA/cosA-sinA

1 answer

1/cos^2A -sin^2A + 2cosAsinA/cos^2A -sin^2A = 1+2cosAsinA/cos^2A -sin^2A

I used the trig identies to expand 1/cos2A and sin2A/cos2A and added the together because they have the same denominator.
How I got from 1 to cos^2+sin^2 is by trig identity cos^2+sin^2=1.

1+2cosAsinA/cos^2A -sin^2A ==> cos^2+sin^2+2cosAsinA/cos^2A -sin^2A (factorise this equation both the numerator and denominator which will give you the following: )

(cosA+sinA)(cosA+sinA)/(cosA+sinA)(cosA-sinA) (Cancel out the common factors)

cosA+sinA/cosA-sinA

Hope this makes sense!