Is cot(θ)+1=csc(θ)(cos(θ)+sin(θ)) ?

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

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prove cot(θ)+1=csc(θ)(cos(θ)+sin(θ))

prove

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

True

Solution steps

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

Manipulating left side

cot (θ) + 1

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

cos^{5} (x) = (1 - sin^{2} (x))^{2} cos (x)

\frac{1}{1 - sin ( x )} = sec^{2} (x) + sec (x) tan (x)

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

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

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

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