Is (1-sin^2(a))(1+tan^2(a))=1 ?

The answer to whether (1-sin^2(a))(1+tan^2(a))=1 is True

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prove (1-sin^2(a))(1+tan^2(a))=1

prove

(1 - sin^{2} (a)) (1 + tan^{2} (a)) = 1

True

Solution steps

(1 - sin^{2} (a)) (1 + tan^{2} (a)) = 1

Manipulating left side

(1 - sin^{2} (a)) (1 + tan^{2} (a))

Rewrite using trig identities

= cos^{2} (a) (1 + tan^{2} (a))

Express with sin, cos

= cos^{2} (a) + sin^{2} (a)

Rewrite using trig identities

= 1

We showed that the two sides could take the same form

\Rightarrow True

sin^{2} (x) + sin^{2} (x) cot^{2} (x) = 1

tan (x) = \frac{1}{cot ( x )}

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

cot (t) csc (t) = \frac{csc ^{2} ( t ) - 1}{cos ( t )}

\frac{1}{1 + sin ( t )} = (sec (t) - tan (t)) sec (t)

Is (1-sin^2(a))(1+tan^2(a))=1 ?
The answer to whether (1-sin^2(a))(1+tan^2(a))=1 is True