InterviewSolution
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InterviewSolution
| 1. |
(cosA-sinA+1)/(cosA+sinA-1)=cosecA+cotA |
| Answer» {tex}L H S=\\frac{\\cos A-\\sin A+1}{\\cos A+\\sin A-1}{/tex}{tex}=\\frac{\\sin A(\\cos A-\\sin A+1)}{\\sin A(\\cos A+\\sin A-1)}{/tex}{tex}=\\frac{\\sin A \\cos A-\\sin ^{2} A+\\sin A}{\\sin A(\\cos A+\\sin A-1)}{/tex}{tex}=\\frac{\\sin A \\cos A+\\sin A-\\left(1-\\cos ^{2} A\\right)}{\\sin A(\\cos A+\\sin A-1)}{/tex}{tex}=\\frac{\\sin A(\\cos A+1)-(1-\\cos A)(1+\\cos A)}{\\sin A(\\cos A+\\sin A-1)}{/tex}{tex}=\\frac{(1+\\cos A)(\\sin A+\\cos A-1)}{\\sin A(\\cos A+\\sin A-1)}{/tex}{tex}=\\frac{(1+\\cos A)(\\sin A+\\cos A-1)}{\\sin A(\\cos A+\\sin A-1)}{/tex}{tex}=\\frac{1}{\\sin A}+\\frac{\\cos A}{\\sin A}{/tex}= cos A + cot A = RHSProved | |