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

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

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prove (sin(x)) 1/(sin(x))=1

prove

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

True

Solution steps

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

Manipulating left side

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

Simplify

\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{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

cos (x) = \frac{cot ( x )}{csc ( x ) - sin ( x )}

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

\frac{1 + sin ( x )}{cos ( x ) tan ( x ) - 1} = - 1

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

cot (x) + 5 = 5 + csc (x) \cdot cos (x)