Cot x sec4x = coy x + 2 tan x + tan3x

Step-by-step explanation:

Simplify RHS

Cotx + 2tanx+tan^3x

Cotx/sinx+2 (sinx/cosx) + sin^3x/cos^3x

Taking LCM

(cos^4x+2sin^2xcos^2x+sin^4x) / sinx cos^3x

(Cos^2x+sin^2x) ^2/sinx cos^3x

(1/sinx cos^3x)

(1/sinx cos^3x) * (cosx/cosx)

Cotx sec^4x

LHS=RHS

Hence proved