Question

How do you solve: sin(π/2-x)/cos(π/2-x) ?

Answer 1

`cotx`

Explanation:

Apply sine and cosine difference identities:
`sin(π/2-x)/cos(π/2-x)`

`(sin(pi/2)*cosx-cos(pi/2)*sinx)/(cos(pi/2)*cosx+sin(pi/2)*sinx)`

Simplify:

`(1*cosx-0*sinx)/(0*cosx+1*sinx)`

`cosx/sinx`

Apply quotient identity:
`cosx/sinx= cotx`