Is sec^2(x)-1=(tan(x))/(cot(x)) ?

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

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prove sec^2(x)-1=(tan(x))/(cot(x))

prove

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

True

Solution steps

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

Manipulating left side

sec^{2} (x) - 1

Express with sin, cos

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

Rewrite using trig identities

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

Manipulating right side

\frac{tan ( x )}{cot ( x )}

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

sec (θ) cos (θ) = 1

cot (θ) (cot (θ) + tan (θ)) = csc^{2} (θ)

cos (\frac{π}{2} + y) = - sin (y)

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

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

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