Is sin^2(x+pi/4)-cos^2(x-pi/4)=0 ?

The answer to whether sin^2(x+pi/4)-cos^2(x-pi/4)=0 is True

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prove sin^2(x+pi/4)-cos^2(x-pi/4)=0

prove

sin^{2} (x + \frac{π}{4}) - cos^{2} (x - \frac{π}{4}) = 0

True

Solution steps

sin^{2} (x + \frac{π}{4}) - cos^{2} (x - \frac{π}{4}) = 0

Manipulating left side

sin^{2} (x + \frac{π}{4}) - cos^{2} (x - \frac{π}{4})

Rewrite using trig identities

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

Rewrite using trig identities

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

Add similar elements:

(\frac{2 sin ( x ) + 2 cos ( x )}{2})^{2} - (\frac{2 cos ( x ) + 2 sin ( x )}{2})^{2} = 0

= 0

We showed that the two sides could take the same form

\Rightarrow True

tan^{2} (u) - sin^{2} (u) = tan^{2} (u) sin^{2} (u)

cos (x) - cos (x) sin^{2} (x) = cos^{3} (x)

sin^{2} (\frac{x}{2}) = \frac{1 - cos ( x )}{2}

cos (x + \frac{3 π}{2}) = sin (x)

1 - tan^{4} (A) = 2 sec^{2} (A) - sec^{4} (A)

Is sin^2(x+pi/4)-cos^2(x-pi/4)=0 ?
The answer to whether sin^2(x+pi/4)-cos^2(x-pi/4)=0 is True