prove that sin2X/secX=2cos^2X/cscX

Question

Also if you can do 

 

Prove that sin (x+y) cos (x-y)= sinX/secX + cosY/cscY

Answer 1

sin 2x / sec x = 2 cos² x / csc x

sin 2x / (1/cos x) = 2 cos2 x / csc x

sin 2x cos x = 2 cos2 x / csc x

(2sin x cos x) cos x = 2 cos2 x / csc x

2 sin x cos² x = 2 cos2 x / csc x

2 cos² x / (1/sin x) = 2 cos2 x / csc x

2 cos² x / csc x = 2 cos2 x / csc x