SOLUTION: prove that (sinx-1)(tanx+secx)= -cosx

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Question 713946: prove that (sinx-1)(tanx+secx)= -cosx
Answer by lwsshak3(11628) About Me  (Show Source):
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prove that (sinx-1)(tanx+secx)= -cosx
start with left side:
(sinx-1)(tanx+secx)=(sinx-1)[(sinx/cosx)+(1/cosx)]
=(sinx-1)(sinx+1)/cosx)
=(sin^2x-1)/cosx
=-(1-sin^2x)/cosx
=-cos^2x/cosx
=-cosx
verified: left side=right side