Is cos(θ)sec(pi/2-θ)=cot(θ) ?

The answer to whether cos(θ)sec(pi/2-θ)=cot(θ) is True

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prove cos(θ)sec(pi/2-θ)=cot(θ)

prove

cos (θ) sec (\frac{π}{2} - θ) = cot (θ)

True

Solution steps

cos (θ) sec (\frac{π}{2} - θ) = cot (θ)

Manipulating left side

cos (θ) sec (\frac{π}{2} - θ)

Rewrite using trig identities

= cos (θ) \frac{1}{sin ( θ )}

Simplify

cos (θ) \frac{1}{sin ( θ )} : \frac{cos ( θ )}{sin ( θ )}

= \frac{cos ( θ )}{sin ( θ )}

Use the basic trigonometric identity:

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

= cot (θ)

We showed that the two sides could take the same form

\Rightarrow True

csc (x) (1 + sin (x)) = 1 + csc (x)

sin (x + y) sin (x - y) = sin (2 x) - sin (2 y)

csc^{2} (x) = 1 - cot^{2} (x)

cos^{2} (θ) = 1 + sin^{2} (θ)

tan^{2} (x) csc^{2} (x) = tan^{2} (x) + 1

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