Is (cos(pi-x))/(cos(pi/2+x))=cot(x) ?

The answer to whether (cos(pi-x))/(cos(pi/2+x))=cot(x) is True

Popular >

prove (cos(pi-x))/(cos(pi/2+x))=cot(x)

prove

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

True

Solution steps

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

Manipulating left side

\frac{cos ( π - x )}{cos ( \frac{π}{2} + x )}

Rewrite using trig identities

= \frac{cos ( π - x )}{- sin ( x )}

Rewrite using trig identities

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

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \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

cos^{2} (x) (sec (x) + 1)^{2} = (1 + cos (x))^{2}

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

sin (a) = cos (9 0^{\circ} + a)

cot (θ) + tan (θ) = 2 csc (2 θ)

tan^{2} (a) - sin^{2} (a) = tan^{2} (a) sin^{2} (a)

Is (cos(pi-x))/(cos(pi/2+x))=cot(x) ?
The answer to whether (cos(pi-x))/(cos(pi/2+x))=cot(x) is True