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

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

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

prove

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

True

Solution steps

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

Manipulating right 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

cos^{2} (x) + cos^{2} (x) cot^{2} (x) = cot^{2} (x)

\frac{1 - cos ^{4} ( x )}{sin ^{2} ( x )} = 1 + cos^{2} (x)

2 cot^{2} (A) sin^{2} (A) = 1 + cos (2 A)

sin (x) + cos (x) = cos (x) (1 + tan (x))

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

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