Is cos(t)sec(pi/2-t)=cot(t) ?

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

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prove cos(t)sec(pi/2-t)=cot(t)

prove

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

True

Solution steps

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

Manipulating left side

cos (t) sec (\frac{π}{2} - t)

Rewrite using trig identities

= cos (t) \frac{1}{sin ( t )}

Simplify

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

= \frac{cos ( t )}{sin ( t )}

Use the basic trigonometric identity:

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

= cot (t)

We showed that the two sides could take the same form

\Rightarrow True

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

cot^{2} (α) = cos^{2} (α) + (cot (α) cos (α))^{2}

cos^{4} (β) - sin^{4} (β) = 2 cos^{2} (β) - 1

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

sec^{2} (x) (1 - cos^{2} (x)) = tan^{2} (x)

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