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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

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

Simplify

(sin^{2} (x))^{2} : sin^{4} (x)

(sin^{2} (x))^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= sin^{2 \cdot 2} (x)

Multiply the numbers:

2 \cdot 2 = 4

= sin^{4} (x)

= sin^{4} (x)

= sin^{4} (x)

We showed that the two sides could take the same form

\Rightarrow True

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