# Prove that: [CBSE 2011]

To prove: Let, y = let, x = cos 2θ

θ = 1/2 cos-1 x …(1)

we know that-

1 + cos 2θ = 2cos2θ

And 1 – cos 2θ = 2sin2θ

y = y = y = y = y = y = We know that: tan(x - y) = y = y = {from 1}

From basic ITF formula we know that –

tan-1(tan x) = x if x (-π/2 , π/2)

Given,

(-1/√2) ≤ x ≤ 1

0 ≤ cos-1x ≤ 3π/4

-3π/8 ≤ -(1/2)cos‑1x ≤ 0

-π/8 < π/4 – (1/2)cos-1x ≤ π/4

Thus, y = , Rate this question :

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