Question : If $A+\frac{1}{1+\frac{1}{2+\frac{1}{3}}}=\frac{9}{10}$, then the value of A is:
Option 1: $\frac{1}{5}$
Option 2: $\frac{3}{10}$
Option 3: $\frac{2}{5}$
Option 4: $\frac{1}{10}$
Correct Answer: $\frac{1}{5}$
Solution : Given: $A+\frac{1}{1+\frac{1}{2+\frac{1}{3}}}=\frac{9}{10}$ ⇒ $A+\frac{1}{1+\frac{1}{\frac{7}{3}}}=\frac{9}{10}$ ⇒ $A+\frac{1}{1+\frac{3}{7}}=\frac{9}{10}$ ⇒ $A+\frac{1}{\frac{10}{7}}=\frac{9}{10}$ ⇒ $A+\frac{7}{10}=\frac{9}{10}$ ⇒ $A=\frac{9}{10}-\frac{7}{10}=\frac{2}{10}=\frac{1}{5}$ Hence, the correct answer is $\frac{1}{5}$.
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Question : If $\tan A=\frac{2}{5}$, then find the value of $\frac{\sec ^2 A}{\operatorname{cosec}^2 A}$.
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Question : The value of $\frac{2}{3} \div \frac{3}{10}$ of $\frac{4}{9}-\frac{4}{5} \times 1 \frac{1}{9} \div \frac{8}{15}-\frac{3}{4}+\frac{3}{4} \div \frac{1}{2}$ is:
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