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

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

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

simplify

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

sin (2 x)

Solution steps

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

Simplify

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

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

Use the basic trigonometric identity:

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

= 2 sin^{2} (x) cot (x)

Express with sin, cos

= 2 cos (x) sin (x)

Rewrite using trig identities

= sin (2 x)

(10 n + 4 n^{7} - 5 n^{6}) - (11 n^{6} + 7 n^{7} - 18 n)

\frac{x ^{2} - 18 x + 80}{x ^{2} - 16 x + 60}

\frac{x ^{2} - 3 x - 4}{x ^{2} + 4 x + 3}

(t^{2} + 2 t + 1)^{2}

2 (3^{x})

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