Given-that-1-1-x-tan-x-1-1-x-Then-find-sin-4x-

Question Number 62109 by sandhyavs last updated on 15/Jun/19

G i v e n t h a t

(1 + \sqrt{1 + x}) \tan x = (1 + \sqrt{1 - x}) .

T h e n f i n d \sin 4 x .

Commented by sandhyavs last updated on 15/Jun/19

A l s o t e l l m e t h e s t e p s . P l e a s e \dots

Commented by sandhyavs last updated on 15/Jun/19

p l e a s e a n s w e r m e \dots

Answered by MJS last updated on 15/Jun/19

\tan x = t

(1 + \sqrt{1 + x}) t = 1 + \sqrt{1 - x}

\sqrt{1 - x} - t \sqrt{1 + x} = t - 1

squaring and transforming

2 t \sqrt{1 - x} \sqrt{1 + x} = (t^{2} - 1) x + 2 t

squaring and transforming

({(t^{2} + 1)}^{2} x + 4 t (t^{2} - 1)) x = 0

\Rightarrow x = 0 \lor x = \frac{4 t (1 - t) (1 + t)}{{(t^{2} + 1)}^{2}}

t = \tan x

x = 4 \sin x \cos x (\cos^{2} x - \sin^{2} x) = \sin 4 x

Commented by sandhyavs last updated on 15/Jun/19

t h a n k y o u s o m u c h .