Is cot^2(α)+1= 1/(sin^2(α)) ?

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

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prove cot^2(α)+1= 1/(sin^2(α))

prove

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

True

Solution steps

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

Manipulating left side

cot^{2} (α) + 1

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{sin ^{2} ( α )}

We showed that the two sides could take the same form

\Rightarrow True

sin (3 x) = 3 sin (x) cos^{2} (x) - sin^{3} (x)

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

\frac{cos ( 3 x ) - cos ( 5 x )}{sin ( 3 x ) + sin ( 5 x )} = tan (x)

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

\frac{1 - sin ( θ )}{cos ( θ )} = sec (θ) - tan (θ)

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