What is cos^2(x+45) ?

The solution to cos^2(x+45) is (1-sin(2x))/2

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simplify cos^2(x+45)

simplify

cos^{2} (x + 4 5^{\circ})

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

Solution steps

cos^{2} (x + 4 5^{\circ})

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}

sin (15 t - \frac{2 π}{3})

cos (arctan (- \frac{1}{g}))

cos (8 π + θ)

1 - cos^{2} (t)

1 + tan^{2} (\frac{π}{2} - x)