Is sin^5(x)=(1-2cos^2(x)+cos^4(x))(sin(x)) ?

The answer to whether sin^5(x)=(1-2cos^2(x)+cos^4(x))(sin(x)) is True

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prove sin^5(x)=(1-2cos^2(x)+cos^4(x))(sin(x))

prove

sin^{5} (x) = (1 - 2 cos^{2} (x) + cos^{4} (x)) (sin (x))

True

Solution steps

sin^{5} (x) = (1 - 2 cos^{2} (x) + cos^{4} (x)) sin (x)

Manipulating right side

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

Rewrite using trig identities

= sin^{5} (x)

We showed that the two sides could take the same form

\Rightarrow True

(sin (x) + cos (x))^{2} = 1 + 2 cos (x) sin (x)

2 cos^{2} (x) = 1

\frac{cos ( a )}{sin ( a ) cot ( a )} = 1

2 (cos (3 θ) + 3 cos (θ)) = 8 cos^{3} (θ)

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

Is sin^5(x)=(1-2cos^2(x)+cos^4(x))(sin(x)) ?
The answer to whether sin^5(x)=(1-2cos^2(x)+cos^4(x))(sin(x)) is True