Cosecx(secx-1)-cotx(1-cosx)=tanx-sinx peoof
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Answer:
Step-by-step explanation:
L.H.S= 1/sinx(1/cosx-1)-cosx/sinx(1-cosx)
=> 1/sinx(1-cosx/cosx)-cosx/sinx(1-cosx)
=> 1-cosx/sinxcosx- cosx(1-cosx)/sinx
=> 1-cosx-cos^2x(1-cosx)/sinxcosx
=> 1-cosx-cos^2x+cos^3x/sinxcosx
=> (1-cos^2x)-cosx+cos^3x/sinxcosx
=> sin^2x-cosx(1-cos^2x)/sinxcosx
=> sin^2x-cosxsin^2x/sinxcosx
=> sin^2x/sinxcosx- cosxsin^2x/sinxcosx
=> sinx/cosx-sinx
=> tanx-sinx........
=> R.H.S.......
Hence, Proved!!!
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