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

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

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

prove

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

True

Solution steps

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

Manipulating left side

csc (x) (1 + sin (x))

Express with sin, cos

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

Rewrite using trig identities

csc (x) + 1

= 1 + csc (x)

We showed that the two sides could take the same form

\Rightarrow True

sin (x + y) sin (x - y) = sin (2 x) - sin (2 y)

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

cos^{2} (θ) = 1 + sin^{2} (θ)

tan^{2} (x) csc^{2} (x) = tan^{2} (x) + 1

sin (\frac{5 π}{6}) = \frac{1}{2}

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