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

2 Answers
Sep 11, 2016

(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.

Sep 11, 2016

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