InterviewSolution
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InterviewSolution
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sin AProve the following identity sesec Atan A-1sec ACOSAcot A-1 |
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Answer» sinx / secx + tanx -1 + cosx/ cosecx+ cot-1 =sinx / 1/ cosx + sinx/ cosx -1 +cosx/ 1/ sinx + cosx/ sinx-1 =sinx/(1+sinx-cosx)_/ cosx + cosx/(1+cosx - sinx)/ sinx = sinxcosx/ (1+sinx-cosx) + sinxcosx/(1+cosx-sinx) = sinxcosx(1/1+sinx-cosx) (1/ 1+ cosx-sinx) =sinxcosx(1+sinx-cosx)+(1+cosx-sinx)/ (1)- ( sinx - cosx)^2 = sinxcosx(1+ sinx-cosx+1+ cosx-sinx)/1-( sinx^2+cosx^2-2sinxcosx) = sinxcosx(1+1)/ 1- sinx^2- cosx^2+2sinxcosx / 2sinxcosx =1 |
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