How do you prove (cscx+cotx)2=1+cosx1cosx?

2 Answers
Apr 15, 2015

In this way.

The first member is:

(1sinx+cosxsinx)2=(1+cosx)2sin2x=(1+cosx)21cos2x=

(1+cosx)2(1+cosx)(1cosx)=1+cosx1cosx,

that is the second member.

Apr 15, 2015

(cscx+cotx)2

= (1sinx+cosxsinx)2

= (1+cosx)2sin2x

= (1+cosx)21cos2x

=(1+cosx)2(1+cosx)(1cosx)

= 1+cosx1cosx = RHS