Is 1+cot(θ)=csc(θ)(cos(θ)+sin(θ)) ?

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

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prove 1+cot(θ)=csc(θ)(cos(θ)+sin(θ))

prove

1 + cot (θ) = csc (θ) (cos (θ) + sin (θ))

True

Solution steps

1 + cot (θ) = csc (θ) (cos (θ) + sin (θ))

Manipulating left side

1 + cot (θ)

Express with sin, cos

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

Use the basic trigonometric identity:

\frac{1}{sin ( x )} = csc (x)

= (cos (θ) + sin (θ)) csc (θ)

= csc (θ) (cos (θ) + sin (θ))

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{cos ( a )}{cot ( a )} = sin (a)

tan (θ) + cot (θ) = \frac{2}{sin ( 2 θ )}

\frac{csc ( θ )}{sin ( θ )} = csc^{2} (θ)

2 sin (2 x) = 4 sin (x) cos (x)

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