Is tan^2(x)=(sin^2(x))/(cos^2(x)) ?

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

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prove tan^2(x)=(sin^2(x))/(cos^2(x))

prove

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

True

Solution steps

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

Manipulating left side

tan^{2} (x)

Express with sin, cos

tan^{2} (x)

Use the basic trigonometric identity:

tan (x) = \frac{sin ( x )}{cos ( x )}

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

Simplify

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

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

Apply exponent rule:

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

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

cos (θ) + sin (θ) tan (θ) = sec (θ)

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

(sec (θ) - tan (θ)) (csc (θ) + 1) = cot (θ)

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

cos (θ) csc (θ) = cot (θ)

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