Is sin^2(u)(1+cot^2(u))=1 ?

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

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prove sin^2(u)(1+cot^2(u))=1

prove

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

True

Solution steps

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

Manipulating left side

sin^{2} (u) (1 + cot^{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

(cos (x) - sec (x))^{2} = - sin^{2} (x)

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

sec (θ) - tan (θ) sin (θ) = cos (θ)

csc (θ) = \frac{1}{cos ( θ )}

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

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