Q. 104.5( 10 Votes )

Prove that:
[CBSE 2011]

Answer :

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 = ,

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