Question

if √3 tan x = 3 sin x, find the value of sin² x- cos²x

Answer 1

Soln:

Given,

√3 tan x = 3 sinx

sin² x- cos²x=?

Now,

√3 tan x = 3 sin x

or, √3sinx/cosx=3sinx

or, √3/3=sinx.cosx/sinx

:.1/√3=cosx

Again,

Putting value of cosx, we get;

sin² x- cos²x

=(1-cos²x)-cos²x :. sin²x= (1- cos²x)

={1-(1/√3 )²}-(1/√3 )²

=1-(1/3)-(1/3)

=(3×1-1×1-1×1)/3 :. Taking 3 as L.c.m.

=(3-1-1)/3

=1/3

:. sin² x- cos²x=1/3.