Is 3sin(x)cos(x)=3sin^2(x)cot(x) ?

The answer to whether 3sin(x)cos(x)=3sin^2(x)cot(x) is True

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prove 3sin(x)cos(x)=3sin^2(x)cot(x)

prove

3 sin (x) cos (x) = 3 sin^{2} (x) cot (x)

True

Solution steps

3 sin (x) cos (x) = 3 sin^{2} (x) cot (x)

Manipulating right side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

= 3 \cdot \frac{cos ( x )}{sin ( x )} sin^{2} (x)

Simplify

3 \cdot \frac{cos ( x )}{sin ( x )} sin^{2} (x) : 3 cos (x) sin (x)

3 \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 3 sin ^{2} ( x )}{sin ( x )}

Cancel the common factor:

sin (x)

= 3 cos (x) sin (x)

= 3 cos (x) sin (x)

= 3 cos (x) sin (x)

= 3 sin (x) cos (x)

We showed that the two sides could take the same form

\Rightarrow True

sin (\frac{3 π}{2} - 0) = - cos (0)

sin (x) + cos (2 x) = 4 sin^{2} (x) - 1

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

tan (- θ) = tan (θ)

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

Is 3sin(x)cos(x)=3sin^2(x)cot(x) ?
The answer to whether 3sin(x)cos(x)=3sin^2(x)cot(x) is True