Is sin^4(x)=(sin^2(x))^2 ?

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

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prove sin^4(x)=(sin^2(x))^2

prove

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

True

Solution steps

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

Manipulating right side

(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)

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{cot ( α )}{cos ( α )} = csc (α)

cos^{(2)} (θ) (1 + tan^{(2)} (θ)) = 1

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

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