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

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

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

prove

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

True

Solution steps

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

Manipulating right side

1 + cot (x)

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) (sin (x) + cos (x))

We showed that the two sides could take the same form

\Rightarrow True

(1 - cos^{2} (x)) cot^{2} (x) = cos^{2} (x)

cos (6 x) = 2 cos^{2} (3 x) - 1

tan^{2} (x) - tan^{2} (x) sin^{2} (x) = sin^{2} (x)

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

csc (2 x) = \frac{csc ( x )}{2 cos ( x )}

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