Anonymous
Anonymous asked in Science & MathematicsMathematics · 9 years ago

# Trig identity. cos2x/(1+sin2x)= tan(pi/4-x)?

Can someone help prove this? Steps would be appreciated.

cos2x/(1+sin2x)= tan(pi/4-x)

Relevance
• iceman
Lv 7
9 years ago

LHS = cos2x / (1 + sin2x)

= (cos^2 x - sin^2 x) / (cos^2 x + sin^2 x + 2sin x cos x)

= [(cos x + sin x)(cos x - sin x)] / (cos x + sin x)^2

= (cos x - sin x) / (cos x + sin x) → divide each term by cos x

= (1 - tanx) / (1 + tan x)

= (tan π/4 - tan x) / (1 - tan π/4 tan x)

= tan (π/4 - x) = RHS