Question

Simplify the expression using trig identities:
1. (sin4x - cos4x)/(sin2x -cos2x)

2. (sinx(cotx)+cosx)/(2cotx)

Answer 1

1.
I am sure you mean
(sin^4 x - cos^4 x)/(sin^2 x - cos^2 x)
= (sin^2 x + cos^2 x )((sin^2 x - cos^2 x)/(sin^2 x - cos^2 x)
= (sin^2 x + cos^2 x)
=1

2.
(sinx(cotx)+cosx)/(2cotx)
= (sinx(cosx/sinx) + cosx)/(2cosx/sinx)
= (cosx + cosx)(sinx/(2cosx)
= 2cosx(sinx)/(2cosx)
= sinx