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

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

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

prove

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

True

Solution steps

sin (x) csc (x) = 1

Manipulating left side

sin (x) csc (x)

csc (x) sin (x) = 1

csc (x) sin (x)

Express with sin, cos

csc (x) sin (x)

Use the basic trigonometric identity:

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

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Cancel the common factor:

sin (x)

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

1 + cos (2 t) = cot (t) sin (2 t)

sin (α) = \frac{2 tan ( \frac{α}{2} )}{1 + tan ^{2} ( \frac{α}{2} )}

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

sin (3 x) cos (2 x) - cos (3 x) sin (2 x) = sin (x)

4 cot^{2} (y) (sec^{2} (y) - 1) = 4