Is (2sin^2(x))/(sin(2x))= 1/(cot(x)) ?

The answer to whether (2sin^2(x))/(sin(2x))= 1/(cot(x)) is True

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prove (2sin^2(x))/(sin(2x))= 1/(cot(x))

prove

\frac{2 sin ^{2} ( x )}{sin ( 2 x )} = \frac{1}{cot ( x )}

True

Solution steps

\frac{2 sin ^{2} ( x )}{sin ( 2 x )} = \frac{1}{cot ( x )}

Manipulating left side

\frac{2 sin ^{2} ( x )}{sin ( 2 x )}

Rewrite using trig identities

\frac{2 sin ^{2} ( x )}{sin ( 2 x )}

Use the Double Angle identity:

sin (2 x) = 2 sin (x) cos (x)

= \frac{2 sin ^{2} ( x )}{2 sin ( x ) cos ( x )}

Simplify

\frac{2 sin ^{2} ( x )}{2 sin ( x ) cos ( x )} : \frac{sin ( x )}{cos ( x )}

\frac{2 sin ^{2} ( x )}{2 sin ( x ) cos ( x )}

Divide the numbers:

\frac{2}{2} = 1

= \frac{sin ^{2} ( x )}{sin ( x ) cos ( x )}

Cancel the common factor:

sin (x)

= \frac{sin ( x )}{cos ( x )}

= \frac{sin ( x )}{cos ( x )}

= \frac{sin ( x )}{cos ( x )}

Manipulating right side

\frac{1}{cot ( x )}

Express with sin, cos

\frac{1}{cot ( x )}

Use the basic trigonometric identity:

cot (x) = \frac{cos ( x )}{sin ( x )}

= \frac{1}{\frac{c o s ( x )}{s i n ( x )}}

Simplify

\frac{1}{\frac{c o s ( x )}{s i n ( x )}} : \frac{sin ( x )}{cos ( x )}

\frac{1}{\frac{c o s ( x )}{s i n ( x )}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{sin ( x )}{cos ( x )}

= \frac{sin ( x )}{cos ( x )}

= \frac{sin ( x )}{cos ( x )}

We showed that the two sides could take the same form

\Rightarrow True

csc (x) (csc (x) + sin (- x)) = cot^{2} (x)

tan (x) + cot (x) = (sec (x)) \cdot (csc (x))

\frac{csc ( θ ) sin ( θ )}{cos ( θ )} = sec (θ)

cos (- \frac{π}{4}) = \frac{1}{2}

\frac{tan ( x ) + cot ( x )}{sec ( x ) csc ( x )} = 1

Is (2sin^2(x))/(sin(2x))= 1/(cot(x)) ?
The answer to whether (2sin^2(x))/(sin(2x))= 1/(cot(x)) is True