cosec x (sec x - 1) - cot x (1 - cos x) = tan x - sin x

Prove the Following Identity.

Asked by Anish | 16th Jun, 2018, 08:38: AM

Expert Answer:

cosec x (sec x - 1) - cot x (1 - cos x) = tan x - sin x
begin mathsize 16px style cosecx left parenthesis secx space minus space 1 right parenthesis space minus space cotx space left parenthesis 1 space minus space cosx right parenthesis
equals space 1 over sinx open parentheses 1 over cosx minus 1 close parentheses minus cosx over sinx left parenthesis 1 space minus space cosx right parenthesis
equals 1 over sinxcosx minus 1 over sinx minus cosx over sinx plus fraction numerator cos squared straight x over denominator sinx end fraction
equals fraction numerator 1 minus cosx minus cos squared straight x plus cos cubed straight x over denominator sinxcosx end fraction
equals fraction numerator 1 minus cos squared straight x minus cosx plus cos cubed straight x over denominator sinxcosx end fraction
equals fraction numerator sin squared straight x minus cosx open parentheses 1 minus cos squared straight x close parentheses over denominator sinxcosx end fraction
equals fraction numerator sin squared straight x minus cosx sin squared straight x over denominator sinxcosx end fraction
equals fraction numerator sin squared straight x over denominator sinxcosx end fraction minus fraction numerator cosxsin squared straight x over denominator sinxcosx end fraction
equals sinx over cosx minus sinx
equals tanx minus sinx end style

Answered by Sneha shidid | 18th Jun, 2018, 09:53: AM