Solve \left(1-2\sin ^2\left(x\right)^2\right) 4\sin ^

Evaluate

(1 - 2 sin^{2} (x^{2})) \times 4 sin^{2} (x) cos^{2} (x)

Calculate

(cos (2 x^{2})) \times 4 sin^{2} (x) cos^{2} (x)

Calculate

cos (2 x^{2}) \times 4 sin^{2} (x) cos^{2} (x)

Multiply the terms

4 cos (2 x^{2}) sin^{2} (x) cos^{2} (x)

Use sin^{2} t = 1 - cos^{2} t to transform the expression

4 cos (2 x^{2}) (1 - cos^{2} (x)) cos^{2} (x)

Multiply the terms

4 cos (2 x^{2}) cos^{2} (x) (1 - cos^{2} (x))

Use cos (2 t) = cos^{2} t - sin^{2} t to transform the expression

4 (cos^{2} (x^{2}) - sin^{2} (x^{2})) cos^{2} (x) (1 - cos^{2} (x))

Multiply the terms

4 cos^{2} (x) (cos^{2} (x^{2}) - sin^{2} (x^{2})) (1 - cos^{2} (x))

Use cos^{2} t = 1 - sin^{2} t to transform the expression

4 (1 - sin^{2} (x)) (cos^{2} (x^{2}) - sin^{2} (x^{2})) (1 - cos^{2} (x))

Transform the expression

More Steps

4 (1 - sin^{2} (x)) (1 - 2 sin^{2} (x^{2})) (1 - cos^{2} (x))

Transform the expression

More Steps

4 (1 - sin^{2} (x)) (1 - 2 sin^{2} (x^{2})) sin^{2} (x)

Multiply the terms

4 sin^{2} (x) (1 - sin^{2} (x)) (1 - 2 sin^{2} (x^{2}))

Use 1 - sin^{2} (t) = cos^{2} (t) to transform the expression

4 sin^{2} (x) cos^{2} (x) (1 - 2 sin^{2} (x^{2}))

Use sin^{2} t = 1 - cos^{2} t to transform the expression

4 (1 - cos^{2} (x)) cos^{2} (x) (1 - 2 sin^{2} (x^{2}))

Transform the expression

More Steps

4 (1 - cos^{2} (x)) cos^{2} (x) (- 1 + 2 cos^{2} (x^{2}))

Multiply the terms

4 cos^{2} (x) (1 - cos^{2} (x)) (- 1 + 2 cos^{2} (x^{2}))

Use 2 cos^{2} t = cos (2 t) + 1 to transform the expression

4 \times \frac{1 + cos ( 2 x )}{2} \times (1 - cos^{2} (x)) (- 1 + 2 cos^{2} (x^{2}))

Transform the expression

More Steps

4 \times \frac{1 + cos ( 2 x )}{2} \times \frac{1 - cos ( 2 x )}{2} \times (- 1 + 2 cos^{2} (x^{2}))

Transform the expression

More Steps

4 \times \frac{1 + cos ( 2 x )}{2} \times \frac{1 - cos ( 2 x )}{2} \times cos (2 x^{2})

Multiply the terms

More Steps

(2 + 2 cos (2 x)) \times \frac{1 - cos ( 2 x )}{2} \times cos (2 x^{2})

Multiply the terms

More Steps

(1 + cos (2 x)) (1 - cos (2 x)) cos (2 x^{2})

Transform the expression

cos (2 x^{2}) - cos (2 x^{2}) cos^{2} (2 x)

Use cos^{2} t = 1 - sin^{2} t to transform the expression

cos (2 x^{2}) - cos (2 x^{2}) (1 - sin^{2} (2 x))

Solution

sin^{2} (2 x) cos (2 x^{2})

Simplify the expression