Question

Prove that cosA(cotA-tanA)=cosecA-2sinA

Answer 1

L.H.S = cosA(cotA - tanA) R.H.S = cosecA - 2sin let us remove thee alphabet 'A' so it would be easy to calculateL.H.S = cos(_cos- sin)

sin cos

= cos ( cos^2 - sin^2)

sin x cos

= cos^2- sin^2

sin

= (1-sin^2) - sin^2

sin

= 1 -2sin^2

sin

= 1 - 2sin^2

sin sin

= cosec A -2 SinA

BECAUSE { 1/ sinA = cosec A and 2sin^2/ sin = 2sin A }

thus L.H.S. = R.H.S PROVED