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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

= cos (x) cot (\frac{π}{2} + x)

Rewrite using trig identities

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

Simplify

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

= - sin (x)

We showed that the two sides could take the same form

\Rightarrow True

cos (x) \cdot csc (x) \cdot tan (x) = 1

- 2 sin (2 (x + 45)) = 2 cos (2 x)

cos^{2} (x) \frac{1}{cos ^{2} ( x )} = 1

(sin (\frac{4 π}{3})) = - \frac{3}{2}

sec (x) - sin^{2} (x) = cos (x)

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