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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

= \frac{cos ( x )}{sin ( π - x )}

Rewrite using trig identities

= \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 (x) \cdot csc (x) = cot (x)

sin (4 x) = 4 sin (x) cos (x) cos (2 x)

\frac{cot ( - θ )}{csc ( θ )} = - cos (θ)

sec (α) - cos (α) = sin (α) tan (α)

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

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