If text{cosec } A + cot A = frac{11}{2}, then | vedclass

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(C) We know that $	ext{cosec}^2 A - \cot^2 A = 1.$Using the identity $a^2 - b^2 = (a - b)(a + b),$ we have $(	ext{cosec } A - \cot A)(	ext{cosec }

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$\frac{44}{117}$

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(C) We know that $	ext{cosec}^2 A - \cot^2 A = 1.$Using the identity $a^2 - b^2 = (a - b)(a + b),$ we have $(	ext{cosec } A - \cot A)(	ext{cosec } A + \cot A) = 1.$Given $	ext{cosec } A + \cot A = \frac{11}{2},$ we substitute this into the identity:$(	ext{cosec } A - \cot A) 	imes \frac{11}{2} = 1 \Rightarrow 	ext{cosec } A - \cot A = \frac{2}{11}.$Now,subtract the two equations:$(	ext{cosec } A + \cot A) - (	ext{cosec } A - \cot A) = \frac{11}{2} - \frac{2}{11}.$$2 \cot A = \frac{121 - 4}{22} = \frac{117}{22}.$$\cot A = \frac{117}{44}.$Since $	an A = \frac{1}{\cot A},$ we get $	an A = \frac{44}{117}.$

If $\text{cosec } A + \cot A = \frac{11}{2},$ then $\tan A = $

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