# 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 :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Inverse Trigonometric Functions - 0161 mins
Inverse Trigonometric Functions - 0242 mins
Inverse Trigonometric Functions - 0339 mins
Inverse Trigonometric Functions - 0438 mins
Questions Practice of Inverse trigonometric Functions30 mins
Interactive Quiz | Graphs of inverse trigo functions39 mins
Graphs of inverse trigo functions48 mins
Functions - 0152 mins
Functions - 0253 mins
Functions - 0361 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

Solve the following equation for x :

Mathematics - Board Papers