What is (csc(a))/(1+cot^2(a)) ?

The solution to (csc(a))/(1+cot^2(a)) is sin(a)

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simplify (csc(a))/(1+cot^2(a))

simplify

\frac{csc ( a )}{1 + cot ^{2} ( a )}

sin (a)

Solution steps

\frac{csc ( a )}{1 + cot ^{2} ( a )}

Simplify

1 + cot^{2} (a) : csc^{2} (a)

= \frac{csc ( a )}{csc ^{2} ( a )}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

csc^{2} (a) = csc (a) csc (a)

= \frac{csc ( a )}{csc ( a ) csc ( a )}

Cancel the common factor:

csc (a)

= \frac{1}{csc ( a )}

Use the basic trigonometric identity:

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

= sin (a)

\frac{ab - a}{b ^{2} - b}

\frac{1}{4} (8 x - 4)

(7 x - 4) (x^{3} - x^{2} + 6)

\frac{20}{72}