Prove the trigonometric identity.

Question

tan x+cot x/csc x cos x=sec^2 x



__= sec^2x

__= sec^2x

__ = sec^2x

__= sec^2x

__ = sec^2x



1/cos^2x=sec^2x

sec^2x=sec^2x

Answer 1

I am sure you meant
(tan x+cot x)/(csc x cos x) = sec^2 x , or else it is not an identity the ways you typed it

LS =(sinx/cosx + cosx/sinx)/(1/sinx * cosx)
= ( (sin^2 x + cos^2 x)/(sinxcosx) )/(cosx/sinx)
= (1/sinxcosx)(sinx/cosx)
= 1/ cos^2 x
= sec^2 x
= RS