Is cos^7(x)=(1-sin^2(x))^3cos(x) ?

The answer to whether cos^7(x)=(1-sin^2(x))^3cos(x) is True

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prove cos^7(x)=(1-sin^2(x))^3cos(x)

prove

cos^{7} (x) = (1 - sin^{2} (x))^{3} cos (x)

True

Solution steps

cos^{7} (x) = (1 - sin^{2} (x))^{3} cos (x)

Manipulating right side

(1 - sin^{2} (x))^{3} cos (x)

Rewrite using trig identities

= cos^{7} (x)

We showed that the two sides could take the same form

\Rightarrow True

(1 + tan (θ))^{2} = sec^{2} (θ) + 2 tan (θ)

\frac{1 + cot ^{2} ( x )}{2 cot ( x )} = csc (2 x)

\frac{sin ( θ )}{1 - sin ^{2} ( θ )} = sec (θ) tan (θ)

sin^{2} (θ) cot^{2} (θ) = 1

tan^{2} (x) = csc^{2} (x) tan^{2} (x) - 1

Is cos^7(x)=(1-sin^2(x))^3cos(x) ?
The answer to whether cos^7(x)=(1-sin^2(x))^3cos(x) is True