Is tan(θ)(cot(θ)+tan(θ))=sec^2(θ) ?

The answer to whether tan(θ)(cot(θ)+tan(θ))=sec^2(θ) is True

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prove tan(θ)(cot(θ)+tan(θ))=sec^2(θ)

prove

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

True

Solution steps

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

Manipulating left side

tan (θ) (cot (θ) + tan (θ))

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{cos ^{2} ( θ )}

Rewrite using trig identities

sec^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

sec^{2} (- θ) - 1 = tan^{2} (θ)

2 tan (x) = \frac{cos ( x )}{csc ( x ) - 1} + \frac{cos ( x )}{csc ( x ) + 1}

sin (- θ) sec (- θ) cot (- θ) = 1

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

cot (x) sin (x) sec^{2} (x) = sec (x)

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