2)Prove the following identities:

Question

a)(cosecx + cotx)(cosecx - cotx) = cotxtanx

b)2/1+sinx + 1/1-sinx = 3sec^2x - tanxcosecx

Answer 1

a) (cscx + cotx)(cscx - cotx)
= csc^2x - cot^2x
= 1/sin^2x - cos^2/sin^2x
= (1-cos^2x)/sin^2x = 1

cotx*tanx also = 1

Answer 2

I will do the second one

2/(1+sinx) + 1/(1-sinx) = 3sec^2x - tanxcosecx

L.S.
= (2(1-sinx) + 1(1+sinx))/(1-sin^2 x)
= (3 - sinx)/cos^2 x
= 3/cos^2 x - sinx/cos^2 x
= 3sec^2 x - (sinx/cos)*1/cosx
= 3sec^2 x - (tanx)(cscx)
= R.S.

Answer 3

thankyou so much !
:)
truly appreciate the help