If CosecA+cotA=mShow that - M square - 1 / 1 + m square =cosA

1.	If CosecA+cotA=mShow that - M square - 1 / 1 + m square =cosA
Answer» Given: cosec A + cot A = m{tex}\\Rightarrow{/tex}\xa0(cosec A + cot A)2 = (m)2 \xa0[squaring both sides ]{tex}\\Rightarrow{/tex}\xa0cosec2A + cot2A + 2 cosec A cot A = m2\xa0\xa0.......(1)Now, LHS\xa0{tex}=\\frac{m^{2}-1}{m^{2}+1}{/tex}{tex}=\\frac{\\ cosec ^{2} A+\\cot ^{2} A+2 \\ cosec A \\cot A-1}{\\ cosec ^{2} A+\\cot ^{2} A+2 \\ cosce A \\cdot \\cot A+1}{/tex}. [ From (1) ]{tex}=\\frac{\\cot ^{2} A+\\cot ^{2} A+2 \\ cosec A \\cdot \\cot A}{\\ cosec ^{2} A+\\ cosec ^{2} A+2 \\ cosec A \\cdot \\cot A}{/tex} [Since, Cosec2A - Cot2A = 1]{tex}=\\frac{2 \\cot ^{2} A+2 \\ cosec A \\cot A}{2 \\ cosec ^{2} A+2 \\ cosec A \\cot A}{/tex}{tex}=\\frac{2 \\cot A(\\cot A+\\ cosec A)}{2 \\ cosec A(\\ cosec A+\\cot A)}{/tex}{tex}=\\frac{\\cot A}{cosec A}{/tex}{tex}=\\frac{\\frac{\\cos A}{\\sin A}}{\\frac{1}{\\sin A}}{/tex}{tex}=\\frac{\\cos A}{\\sin A} \\times \\frac{\\sin A}{1}{/tex}= cos A = RHSHence, Proved.

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