Question

cos^2θ/1+sin^2θ.=cot(π/4+θ.)​ prove this

Answer 1

Answer:

we know,

sin2A = 2sinA.cosA

cos2A = 1–2sin²A = 2cos²A-1 = cos²A-sin²A

sin²A+cos²A = 1

tan(x-y) = (tanx-tiny)/(1+tanx.tany)

To prove : Cos 2θ/ (1 +Sin 2θ) = tan (π /4 – θ)

L.H.S.

cos2θ/(1+sin 2θ)

= (cos²θ-sin²θ)/(1 +2sinθ.cosθ)

= (cosθ+sinθ)(cosθ-sinθ)/ (cos²θ+sin²θ+2sinθ.cosθ)

= (cosθ+sinθ)(cosθ-sinθ)/(cosθ+sinθ)²

= (cosθ-sinθ)/(cosθ+sinθ)

Dividing the numerator and denominator by cosθ

= (1-tanθ)/(1+tanθ)

= (tanπ/4-tanθ)/(1+tanπ/4.tanθ)

= tan(π/4-θ) = R.H.S.

Step-by-step explanation:

I hope it will help uhhh