Is 1/(sin(θ))=sin(θ)+cos(θ)cot(θ) ?

The answer to whether 1/(sin(θ))=sin(θ)+cos(θ)cot(θ) is True

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prove 1/(sin(θ))=sin(θ)+cos(θ)cot(θ)

prove

\frac{1}{sin ( θ )} = sin (θ) + cos (θ) cot (θ)

True

Solution steps

\frac{1}{sin ( θ )} = sin (θ) + cos (θ) cot (θ)

Manipulating right side

sin (θ) + cos (θ) cot (θ)

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{sin ( θ )}

We showed that the two sides could take the same form

\Rightarrow True

cos (a) cos (b) = \frac{1}{2} (cos (a - b) + cos (a + b))

sin^{2} (θ) (cot^{2} (θ) + 1) = 1

sin (a - b) = sin (a) cos (b) - cos (a) sin (b)

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

2 + sec (A) cos (A) = 3

Is 1/(sin(θ))=sin(θ)+cos(θ)cot(θ) ?
The answer to whether 1/(sin(θ))=sin(θ)+cos(θ)cot(θ) is True