Question

How do you use sum and difference identities to simplify `csc(pi/2 +x) - sec(pi - x)`?

Answer 1

0

Explanation:

`csc(theta) = 1/sin(theta) , sec(theta) = 1/cos(theta)`
`1/(sin(pi/2 + x)) - 1/(cos(pi - x))`

`sin(a+b) = sina*cosb + cosa * sin b`
`cos(a - b) = cosa*cosb + sina * sinb`

`1/(sin(pi/2) *cosx + cos(pi/2)*sinx) - 1/(cospi*cosx + sinpi*sinx)`
Using either calculator or unit circle,
`cos(pi/2) = 0, sin(pi) = 0, cos(pi) = 1, sin(pi/2) = 1`

`1/(cosx) - 1/(cosx) = 0`