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

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

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

prove

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

True

Solution steps

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

Manipulating left side

2 cot (x) sin (x)

Express with sin, cos

2 cot (x) sin (x)

Use the basic trigonometric identity:

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

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

Simplify

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

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

Multiply fractions:

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

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

Cancel the common factor:

sin (x)

= cos (x) \cdot 2

= 2 cos (x)

= 2 cos (x)

We showed that the two sides could take the same form

\Rightarrow True

p ro v e cos (3 x) = cos (x) (4 cos^{2} (x) - 3)

p ro v e \frac{1}{sin ( x ) cot ( x )} = sec (x)

p ro v e csc (θ) + sin (θ) = \frac{2 - cos ^{2} ( θ )}{sin ( θ )}

p ro v e tan^{2} (x) - sin^{2} (x) = tan^{2} (x)

p ro v e sin (x) ((1 + cot^{2} (x))) = csc (x)