How do you verify #(sinx + cosx) / (sinx - cosx) = (secx + cscx) / (secx - cscx)#?

1 Answer
Nghi N.
Nov 4, 2015

Verify trig expression.

Explanation:

Transform the numerator of the right side:
#1/(cos x) + 1/(sin x) = (sin x + cos x)/(sin x.cos x)# (1).
Transform the denominator of the right side:
#1/(cos x) - 1/(sin x) = (sin x - cos x)/(sin x.cos x)# (2)
The right side becomes:
#((sin x + cos x)/(sin x.cos x))((sin x.cos x)/(sin x - cos x))#
#= (sin x + cos x)/(sin x - cos x)#

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