Question

Hi, I need a bit of help with verifying identities. The problems are as follows:

sinx+cosx/cotx+1=sinx
sin2x/sin - cos2x/cosx=secx
1-tan^2θ/1+tan^2θ=cos2θ

Answer 1

sin x + cos x / cos x/sin x +1 = ?
sin x + sin x + 1 = sin x no way
maybe you mean
(sinx+cosx)/ (cotx+1)
(sin x + cos x) / (cos x/sin x + sin x/sin x)
sin x ( sin x + cos x) / (cos x + sin x)
= sin x yes
Parentheses are VITAL !!!!!

Answer 2

sin2x/sin - cos2x/cosx
= 2sinx cosx/sinx - (1-2sin^2x)/cosx
= 2cosx - secx + 2sin^2x/cosx
= (2cos^2x+2sin^2x)/cosx - secx
see if you can finish it from here

1-tan^2θ/1+tan^2θ
= (1-(sec^2θ - 1)/sec^2θ
= (2 - sec^2θ)/sec^2θ
see if you can finish it off from here.