Is sec^2(θ)-1=(tan(θ))/(cot(θ)) ?

The answer to whether sec^2(θ)-1=(tan(θ))/(cot(θ)) is True

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prove sec^2(θ)-1=(tan(θ))/(cot(θ))

prove

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

True

Solution steps

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

Manipulating left side

sec^{2} (θ) - 1

Express with sin, cos

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

Rewrite using trig identities

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

Manipulating right side

\frac{tan ( θ )}{cot ( θ )}

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

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

cos (2 x) = cos (x) cos (x) - sin (x) sin (x)

(\frac{8}{6})^{2} + 1 = (\frac{10}{6})^{2}

sec^{4} (θ) - tan^{4} (θ) = 2 tan^{2} (θ) + 1

tan^{2} (x) (1 + cot^{2} (x)) = sec^{2} (x)

Is sec^2(θ)-1=(tan(θ))/(cot(θ)) ?
The answer to whether sec^2(θ)-1=(tan(θ))/(cot(θ)) is True