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Answer» L.H.S.=(cotx+cosecx-1)/(cotx-cosecx+1) =(cosx/sinx+1/sinx-1)/(cosx/sinx-1/sinx+1) =(cosx+1-sinx)/(cosx-1+sinx) =(2cos^2x/2-2sinx/2cosx/2)/ (-2sin^2x/2+2cosx/2sinx/2) =(2cosx/2(cosx/2-sinx/2))/ (2sinx/2(cosx/2-sinx/2)) =cosx/2/sinx/2 =cotx/2 =R.H.S.Hence Proved. |
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