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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

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

Simplify

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Cancel the common factor:

sin (x)

= 2 cos (x) sin (x)

= 2 cos (x) sin (x)

= 2 cos (x) sin (x)

Rewrite using trig identities

2 cos (x) sin (x)

Use the Double Angle identity:

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

= sin (2 x)

= sin (2 x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1 + tan ( x )}{sin ( x ) + cos ( x )} = sec (x)

cos (x) sec (x) = 1

\frac{sec ( t ) - cos ( t )}{sec ( t )} = sin^{2} (t)

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

sin (\frac{π}{2} - x) = sin (\frac{π}{2} + x)

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