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

2 Answers
Nghi N.
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.

Bio
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#

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