Solve \frac{\sin a}{1-\cot a} \frac{\cos a}{1-\tan a}

Evaluate

\frac{sin ( a )}{1 - cot ( a )} \times \frac{cos ( a )}{1 - tan ( a )}

Multiply the terms

\frac{sin ( a ) cos ( a )}{( 1 - cot ( a ) ) ( 1 - tan ( a ) )}

Transform the expression

More Steps

\frac{sin ( a ) cos ( a )}{\frac{( s i n ( a ) - c o s ( a ) ) ( c o s ( a ) - s i n ( a ) )}{s i n ( a ) c o s ( a )}}

Multiply by the reciprocal

sin (a) cos (a) \times \frac{sin ( a ) cos ( a )}{( sin ( a ) - cos ( a ) ) ( cos ( a ) - sin ( a ) )}

Multiply the terms

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

Multiply the terms

More Steps

\frac{sin ^{2} ( a ) cos ^{2} ( a )}{( sin ( a ) - cos ( a ) ) ( cos ( a ) - sin ( a ) )}

Transform the expression

\frac{( sin ( a ) cos ( a ) ) ^{2}}{2 sin ( a ) cos ( a ) - sin ^{2} ( a ) - cos ^{2} ( a )}

Use 2 sin (t) cos (t) = sin (2 t) to transform the expression

\frac{( sin ( a ) cos ( a ) ) ^{2}}{sin ( 2 a ) - sin ^{2} ( a ) - cos ^{2} ( a )}

Transform the expression

More Steps

\frac{( sin ( a ) cos ( a ) ) ^{2}}{sin ( 2 a ) - 1}

Use sin (2 t) = 2 sin t cos t to transform the expression

\frac{( sin ( a ) cos ( a ) ) ^{2}}{2 cos ( a ) sin ( a ) - 1}

Transform the expression

\frac{( \frac{s i n ( 2 a )}{2} ) ^{2}}{2 cos ( a ) sin ( a ) - 1}

Transform the expression

\frac{( \frac{s i n ( 2 a )}{2} ) ^{2}}{sin ( 2 a ) - 1}

Rewrite the expression

\frac{\frac{s i n ^{2} ( 2 a )}{4}}{sin ( 2 a ) - 1}

Multiply by the reciprocal

\frac{sin ^{2} ( 2 a )}{4} \times \frac{1}{sin ( 2 a ) - 1}

Multiply the terms

\frac{sin ^{2} ( 2 a )}{4 ( sin ( 2 a ) - 1 )}

Solution

More Steps

\frac{sin ^{2} ( 2 a )}{4 sin ( 2 a ) - 4}

Simplify the expression