Question

How do you simplify the expression `(sinx-cosx)/(sinxcosx)`?

Answer 1

`(2sqrt2.sin (x - pi/4))/(sin 2x)`

Explanation:

Use trig identity:
sin 2x = 2sin x.cos x
The expression becomes
`E = (2(sin x - cos x))/(sin 2x)`
Since `sin x - cos x = sqrt2.sin ( x - pi/4)`, there for:
`E = (2sqrt2.sin (x - pi/4))/(sin 2x)`
This simplified form, in the form of 2 products, can be easily solved
in a trig equation.

Answer 2

`frac{sinx-cosx}{sinx cosx} = secx - cscx`

Explanation:

`frac{sinx-cosx}{sinx cosx} = frac{sinx}{sinx cosx} - frac{cosx}{sinx cosx}`

`= frac{1}{cosx} - frac{1}{sinx}`

`= secx - cscx`