Is tan^2(θ)=(sin^2(θ))/(cos^2(θ)) ?

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

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prove tan^2(θ)=(sin^2(θ))/(cos^2(θ))

prove

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

True

Solution steps

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

Manipulating left side

tan^{2} (θ)

Express with sin, cos

tan^{2} (θ)

Use the basic trigonometric identity:

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

= (\frac{sin ( θ )}{cos ( θ )})^{2}

Simplify

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

(\frac{sin ( θ )}{cos ( θ )})^{2}

Apply exponent rule:

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

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

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

sin (x - \frac{π}{6}) + cos (x) = sin (x + π)

tan^{2} (2 3^{\circ}) - sec^{2} (2 3^{\circ}) = - 1

(1 - cos^{2} (t)) (1 + cos^{2} (t)) = 1

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

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