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tu 3upaiateywcps A -sin A+1cos A + sin A -1cos A t sin A1 cosec A+ctsingthe dentiyco0e -1+ sf A |
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Answer» CosA-sinA+1/cosA+sinA-1 =(cosA-sinA+1)(cosA+sinA+1)/(cosA+sinA-1)(cosA+sinA+1) =(cos²A-cosAsinA+cosA+cosAsinA-sin²A+sinA+cosA-sinA+1)/{(cosA+sinA)²-(1)²} =(cos²A-sin²A+2cosA+1)/(cos²A+2cosAsinA+sin²A-1) ={cos²A+2cosA+(1-sin²A)}/(1+2cosAsinA-1) [∵, sin²A+cos²A=1] =(cos²A+2cosA+cos²A)/2cosAsinA =(2cos²A+2cosA)/2cosAsinA =2cosA(cosA+1)/2cosAsinA =(cosA+1)/sinA =cosA/sinA+1/sinA =cotA+cosecA =cosecA+cotA (Proved) |
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