Question

If $ \tan (A+B)=p,\tan (A-B)=q, $ then the value of tan 2A is

• A. $ \frac{p+q}{p-q} $
• B. $ \frac{p-q}{1+pq} $
• C. $ \frac{1+pq}{1-p} $
• D. $ \frac{p+q}{1-pq} $

Answer 1

Answer: (D)

Let $ A=\underset{x\to \infty }{\mathop{\lim }}\,{{x}^{1/x}} $ Taking log on both sides, we get $ \log A=\underset{x\to \infty }{\mathop{\lim }}\,\frac{1}{x}\log x $ $ \Rightarrow $ $ \log A=0 $ $ \left( \because \underset{x\to \infty }{\mathop{\lim }}\,\frac{\log x}{{{x}^{m}}}=0\,\,\forall m>0 \right) $ $ \Rightarrow $ $ A={{e}^{0}}=1 $ $ \Rightarrow $ $ \underset{x\to \infty }{\mathop{\lim }}\,{{x}^{1/x}}=1 $