Is cot(x)+1=csc(x)(cos(x)+sin(x)) ?

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

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prove cot(x)+1=csc(x)(cos(x)+sin(x))

prove

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

True

Solution steps

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

Manipulating left side

cot (x) + 1

Express with sin, cos

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

Use the basic trigonometric identity:

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

= (cos (x) + sin (x)) csc (x)

= csc (x) (cos (x) + sin (x))

We showed that the two sides could take the same form

\Rightarrow True

\frac{csc ( x ) - cot ( x )}{csc ( x )} = 1 - cos (x)

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

sin (θ + \frac{π}{3}) = sin (θ) + sin (\frac{π}{3})

arcsec (x) = cos (x)

(csc (θ) - cot (θ)) (1 + sec (θ)) = tan (θ)

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