Is 1/(cos^2(x))=(1/(cos(x)))^2 ?

The answer to whether 1/(cos^2(x))=(1/(cos(x)))^2 is True

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prove 1/(cos^2(x))=(1/(cos(x)))^2

prove

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

True

Solution steps

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

Manipulating right side

(\frac{1}{cos ( x )})^{2}

Simplify

(\frac{1}{cos ( x )})^{2} : \frac{1}{cos ^{2} ( x )}

(\frac{1}{cos ( x )})^{2}

Apply exponent rule:

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

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

Apply rule

1^{a} = 1

1^{2} = 1

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

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

We showed that the two sides could take the same form

\Rightarrow True

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

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

1 - \frac{( cos ^{2} ( θ ) )}{1 + sin ( θ )} = sin (θ)

tan (18 0^{\circ} - y) = - tan (y)

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

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