Question

formula of sin²x-cos²x​

Answer 1

Answer :

$sin {}^{2} x - cos {}^{2} x = cos2x$

Answer 2

Given,

$sin^{2}x - cos^{2}x$

To Find,

The formula of the given expression.

Solution,

There is no such formula for this expression, $sin^{2}x - cos^{2}x$.

But we can expand it to two forms.

We know $x^{2} -y^{2}$=(x+y)(x-y).

Hence,

$sin^{2}x - cos^{2}x$ = (sinx+cosx)(sinx-cosx).

Otherwise,

$sin^{2}x - cos^{2}x$=($sin^{2}x - cos^{2}x$).1=($sin^{2}x - cos^{2}x$).($sin^{2}x +cos^{2}x$) =$sin^{4}x - cos^{4}x$.

Hence, The formula of  $sin^{2}x - cos^{2}x$ is both =$sin^{4}x - cos^{4}x$ and (sinx+cosx)(sinx-cosx).