Question

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

Answer 1

see explanation

Explanation:

Consider the left side

Using the trigonometric identities

csc x =
`(1)/(sinx)` and sec x =
`(1)/(cosx)`

Note that sin(
`(\pi )/(2)` - x) = cos x

Hence

csc(
`(\pi )/(2)` - x)

=
`(1)/(sin((\pi )/(2)-x) )`

=
`(1)/(cosx)`

= sec x = right side ⇒ proven