Is tan^2(θ)=csc^2(θ)tan^2(θ)-1 ?

The answer to whether tan^2(θ)=csc^2(θ)tan^2(θ)-1 is True

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prove tan^2(θ)=csc^2(θ)tan^2(θ)-1

prove

tan^{2} (θ) = csc^{2} (θ) tan^{2} (θ) - 1

True

Solution steps

tan^{2} (θ) = csc^{2} (θ) tan^{2} (θ) - 1

Manipulating right side

csc^{2} (θ) tan^{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 )}

Rewrite using trig identities

tan^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

cos (x + \frac{π}{6}) + sin (x - \frac{π}{3}) = 0

tanh^{2} (x) + sech^{2} (x) = 1

\frac{cos ( θ ) sec ( θ )}{cot ( θ )} = tan (θ)

csc^{2} (u) - cos (u) sec (u) = cot^{2} (u)

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

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