Is tan^2(A)(csc^2(A)-1)=1 ?

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

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prove tan^2(A)(csc^2(A)-1)=1

prove

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

True

Solution steps

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

Manipulating left side

tan^{2} (A) (csc^{2} (A) - 1)

Express with sin, cos

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

Rewrite using trig identities

= 1

We showed that the two sides could take the same form

\Rightarrow True

cos^{3} (θ) = - 1

1 + cos (x) = \frac{csc ( x ) + cot ( x )}{csc ( x )}

(tan (x)) (sin (x)) + (cos (x)) = sec (x)

cos (k (x) x) = cos (- k (x) x)

tan^{2} (x) = sin^{2} (x) + sin^{2} (x) tan^{2} (x)

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