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

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

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

simplify

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

sin (x)

Solution steps

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

Simplify

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

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

Apply exponent rule:

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

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

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

Cancel the common factor:

csc (x)

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

Use the basic trigonometric identity:

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

= sin (x)

1 2^{3} \cdot 1 2^{4}

4^{2} \cdot 2^{3} \cdot 8^{2}

\frac{( 1 + 3 i ) ( - 3 - i )}{2 - 2 i}

∣ 54 ∣

4 \cdot (- 10)