What is (sin(t+(3pi)/4))^2 ?

The solution to (sin(t+(3pi)/4))^2 is (1-sin(2t))/2

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simplify (sin(t+(3pi)/4))^2

simplify

(sin (t + \frac{3 π}{4}))^{2}

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

Solution steps

sin^{2} (t + \frac{3 π}{4})

Rewrite using trig identities

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

Simplify

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

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

Expand

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

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

Rewrite using trig identities

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

(cos (0) - cos (- π)) d x

3 \cdot cos (x + 2 π) + 15

sin^{3} (x + \frac{3 π}{2})

cos (x) + cos (x - \frac{π}{3})

- sin (p i t - 4 p i t)

What is (sin(t+(3pi)/4))^2 ?
The solution to (sin(t+(3pi)/4))^2 is (1-sin(2t))/2