Is (cos(-x))/(sin(-x))=-cot(x) ?

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Use the negative angle identity:

sin (- x) = - sin (x)

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

Use the negative angle identity:

cos (- x) = cos (x)

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

Simplify

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

Use the basic trigonometric identity:

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

= - cot (x)

We showed that the two sides could take the same form

\Rightarrow True

sin (\frac{9 π}{4}) = cos (\frac{9 π}{4})

tan (β) = csc (β) sec (β) - cot (β)

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

sec^{2} (θ) (1 - sin^{2} (θ)) = sec^{2} (θ)

cos (x - 9 0^{\circ}) = sin (x)

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