Question

Prove the following: 

cos (3π/2 +x) cos (2π+x) [cot(3π/2-x)+ cot (2π+x)]

Answer 1

L.H.S.

= cos (3π/2 +x) cos (2π+x) .[cot(3π/2-x)+ cot (2π+x)] 

= (sin x)(cos x) (tan x + cot x)

= sin x cos x (\((\frac{sin\, x}{cos\, x} + \frac{cos\, x}{sin\,x})\))

= sin x cos x \((\frac{sin^2\, x+cos^2\, x}{sin\,x\,cos\,x})\)

= sin x cos x (\(\frac{1}{sin\, x\, cos\, x}\))

= 1 = R.H.S