What is cos(x)(cos(2x)-2sin^2(x)) ?

The solution to cos(x)(cos(2x)-2sin^2(x)) is 4cos^3(x)-3cos(x)

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simplify cos(x)(cos(2x)-2sin^2(x))

simplify

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

4 cos^{3} (x) - 3 cos (x)

Solution steps

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

Rewrite using trig identities

= (- 3 + 4 cos^{2} (x)) cos (x)

Expand

(- 3 + 4 cos^{2} (x)) cos (x) : - 3 cos (x) + 4 cos^{3} (x)

= 4 cos^{3} (x) - 3 cos (x)

4.5 \cdot 1 0^{9}

4 + \frac{5}{2}

\frac{81}{64}

- 3 x^{2} + 5 x - 2

\frac{4}{3} + \frac{1}{4}

What is cos(x)(cos(2x)-2sin^2(x)) ?
The solution to cos(x)(cos(2x)-2sin^2(x)) is 4cos^3(x)-3cos(x)