Is prove-(cos^2(x))/(sin(x))=-cos(x)cot(x) ?

The answer to whether prove-(cos^2(x))/(sin(x))=-cos(x)cot(x) is True

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prove-(cos^2(x))/(sin(x))=-cos(x)cot(x)

prove

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

True

Solution steps

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

Manipulating right side

- cos (x) cot (x)

Express with sin, cos

- cos (x) cot (x)

Use the basic trigonometric identity:

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

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

Simplify

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

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

Multiply fractions:

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

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

cos (x) cos (x) = cos^{2} (x)

cos (x) cos (x)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

cos (x) cos (x) = cos^{1 + 1} (x)

= cos^{1 + 1} (x)

Add the numbers:

1 + 1 = 2

= cos^{2} (x)

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

tan (2 t) = 2 sin (t) cos (t) sec (2 t)

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

tan^{3} (x) - tan (x) sec^{2} (x) = tan (- x)

sec (π - x) = - sec (x)

sin (- x) - cos (- x) = - (sin (x) + cos (x))

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