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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Express with sin, cos

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

Rewrite using trig identities

= 1

We showed that the two sides could take the same form

\Rightarrow True

sec^{3} (x) = \frac{1}{cos ^{3} ( x )}

sin (x) = \frac{5}{13}

sec (x) - tan (x) \cdot sin (x) = \frac{1}{sec ( x )}

\frac{( 1 + cos ( 2 y ) )}{sin ^{2} ( y )} = 2 cot^{2} (y)

4 cos^{2} (B) - 4 sin^{2} (B) = 4 - 8 sin^{2} (B)

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