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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Simplify

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

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

Apply exponent rule:

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

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

= cos^{2 + 2} (x)

Add the numbers:

2 + 2 = 4

= cos^{4} (x)

= cos^{4} (x)

We showed that the two sides could take the same form

\Rightarrow True

sin (x) = 3 sin (\frac{x}{2})

sin (θ) cos (θ) sec (θ) csc (θ) = 1

sin (\frac{π}{2} - 0) = cos (0)

sin (3 x) = sin (3 - 4 sin^{2} (x))

\frac{tan ^{2} ( θ )}{sec ( θ ) + 1} = sec (θ) - 1

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