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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

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

Rewrite using trig identities

csc (x)

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{1 - ( cos ( x ) )}{sec ( x ) - 1} = cos (x)

sec (θ) cos (θ) csc (θ) = cot (θ)

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

csc^{2} (x) (1 - cos^{2} (x)) = tan (42 0^{\circ})

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