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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

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

Simplify

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

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

Apply exponent rule:

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

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

= cos^{2 + 1} (x)

Add the numbers:

2 + 1 = 3

= cos^{3} (x)

= cos^{3} (x)

= cos^{3} (x)

We showed that the two sides could take the same form

\Rightarrow True

p ro v e tan (3 x) cos (3 x) = sin (3 x)

p ro v e 9 cos^{2} (x) - 9 sin^{2} (x) = 9 - 18 sin^{2} (x)

p ro v e 7 cos^{2} (B) - 7 sin^{2} (B) = 14 cos^{2} (B) - 7

p ro v e \frac{sin ( θ ) csc ( θ )}{tan ( θ )} = cot (θ)

p ro v e sec^{2} (θ) + csc (θ) = - sec^{2} (θ) csc (θ)

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