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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

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

Simplify

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

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

Apply exponent rule:

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

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

= cos^{1 + 2} (x)

Add the numbers:

1 + 2 = 3

= cos^{3} (x)

= cos^{3} (x)

= cos^{3} (x)

We showed that the two sides could take the same form

\Rightarrow True

4 (5 cos (2 x)) + (- 20 cos (2 x)) = 0

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

2 cos (2 x) - 1 = 1 - 2 sin (2 x)

(3 sin (x) - 3 cos (x))^{2} = - 9 sin (2 x) + 9

- 5 cos (0) - 8.6602500000000 \dots sin (0) = - 5

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