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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

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

Simplify

cos^{2} (2 x) cos (2 x) : cos^{3} (2 x)

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

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

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

Add the numbers:

2 + 1 = 3

= cos^{3} (2 x)

= cos^{3} (2 x)

= cos^{3} (2 x)

We showed that the two sides could take the same form

\Rightarrow True

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

tan (18 0^{\circ} - y) = - tan (y)

cot (2 x) = \frac{cot ( 2 x ) - 1}{2 cot ( x )}

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

\frac{1}{csc ^{2} ( x )} = 1 - cos^{2} (x)

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