Unless I see an obvious identity I can replace, I usually change everything to sines and cosines.
LS = (1/cosx - cosx)/(sinx/cosx - sinx)
= ( 1 - cos^2 x)/cosx )/( (sinx - sinxcosx)/cosx )
= ( 1 - cos^2 x)/cosx )* cosx/( (sinx - sinxcosx)
= (1 - cos^2 x)/(sinx(1 - cosx))
= (1 - cosx)(1 + cosx)/(sinx(1 - cosx))
= (1 + cosx)/sinx
= 1/sinx + cosx/sinx
= cscx + cotx
+ RS
(secx-cosx) / (tanx-sinx) = cosecx+cotx
Spent hours to solve this question but failed. Please help. Thank you
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