Is 1/(sin(x)-sin(x)cos(x))=csc(x) ?

The answer to whether 1/(sin(x)-sin(x)cos(x))=csc(x) is False

prove 1/(sin(x)-sin(x)cos(x))=csc(x)

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

\frac{1}{sin ( 1 ) - sin ( 1 ) cos ( 1 )} = 2.58516 \dots

\frac{1}{sin ( 1 ) - sin ( 1 ) cos ( 1 )}

Refine to a decimal form

= 2.58516 \dots

csc (1) = 1.18839 \dots

csc (1)

Refine to a decimal form

= 1.18839 \dots

The two sides are not equal

\Rightarrow False

p ro v e sin (a) csc (a) = 1

p ro v e cos^{2} (θ) = \frac{( 1 + cos ( 2 θ ) )}{2}

p ro v e cos (33 0^{\circ}) = 1 - 2 sin^{2} (16 5^{\circ})

p ro v e tan^{4} (x) = sec^{4} (x) - sec^{2} (x)

p ro v e cot (x) = \frac{- cos ^{2} ( x )}{( sin ( x ) + 1 ) ^{2}}

Is 1/(sin(x)-sin(x)cos(x))=csc(x) ?
The answer to whether 1/(sin(x)-sin(x)cos(x))=csc(x) is False