What is (-cos(pi/4+x))^2 ?

The solution to (-cos(pi/4+x))^2 is (1-sin(2x))/2

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simplify (-cos(pi/4+x))^2

simplify

(- cos (\frac{π}{4} + x))^{2}

\frac{1 - sin ( 2 x )}{2}

Solution steps

(- cos (\frac{π}{4} + x))^{2}

Rewrite using trig identities

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

Simplify

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

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

Expand

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

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

Rewrite using trig identities

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

e^{l n (1 - c o s^{2} (x))}

cos (\frac{π}{6} + x)

sin (- 2 sin (x) cos (x))

cos (arctan (y))

1 + tan^{2} (9 0^{\circ} - x)