Question

Prove csc(pi/2 -x) = sec x

Answer 1

Answer:

see explanation

Step-by-step explanation:

Consider the left side

Using the trigonometric identities

csc x = $\frac{1}{sinx}$ and sec x = $\frac{1}{cosx}$

Note that sin( $\frac{\pi }{2}$ - x) = cos x

Hence

csc($\frac{\pi }{2}$ - x)

= $\frac{1}{sin(\frac{\pi }{2}-x) }$

= $\frac{1}{cosx}$

= sec x = right side ⇒ proven