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

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

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

prove

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

True

Solution steps

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

Manipulating left side

csc (x) sin (\frac{π}{2} - x)

Rewrite using trig identities

= csc (x) cos (x)

Rewrite using trig identities

= cot (x)

We showed that the two sides could take the same form

\Rightarrow True

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

cos (4 θ) = 2 (cos (2 θ))^{2} - 1

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

tan (\frac{x}{2}) = - cot (x) + csc (x)

\frac{1}{csc ^{2} ( x )} + \frac{1}{sec ^{2} ( x )} = 1

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