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

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

Solution

prove

sin (x) \cdot 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

csc^{2} (θ) (1 - cos^{2} (θ)) = sin (648 0^{\circ})

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

\frac{1 + sec ( θ )}{sec ( θ )} = 2 cos^{2} (\frac{θ}{2})

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

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