Is (sin(-x)cot(x))/(sin(pi/2-x))=1 ?

The answer to whether (sin(-x)cot(x))/(sin(pi/2-x))=1 is False

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prove (sin(-x)cot(x))/(sin(pi/2-x))=1

prove

\frac{sin ( - x ) cot ( x )}{sin ( \frac{π}{2} - x )} = 1

False

Solution steps

\frac{sin ( - x ) cot ( x )}{sin ( \frac{π}{2} - x )} = 1

Show that the two sides are not equal

For

\frac{sin ( - x ) cot ( x )}{sin ( \frac{π}{2} - x )} = 1

plug in

x = 1

\frac{sin ( - 1 ) cot ( 1 )}{sin ( \frac{π}{2} - 1 )} = - 1

\frac{sin ( - 1 ) cot ( 1 )}{sin ( \frac{π}{2} - 1 )}

Refine to a decimal form

= - 1

The two sides are not equal

\Rightarrow False

csc^{2} (\frac{θ}{2}) = \frac{2}{1 - cos ( θ )}

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

\frac{tan ^{2} ( θ ) + 1}{sec ( θ )} = sec (θ)

cot^{2} (θ) + 1 = \frac{1}{sin ^{2} ( θ )}

3 cos (2 x + \frac{π}{2}) - 2 = 6 cos^{2} (x + \frac{π}{4})

Is (sin(-x)cot(x))/(sin(pi/2-x))=1 ?
The answer to whether (sin(-x)cot(x))/(sin(pi/2-x))=1 is False