WBJEE · Maths · Trigonometric Ratios & Identities
If \(\cos (\theta+\phi)=\frac{3}{5}\) and \(\sin (\theta-\phi)=\frac{5}{13}, 0 \lt \theta, \phi \lt \frac{\pi}{4}\), then \(\cot (2 \theta)\) has the value
- A \(\frac{16}{63}\)
- B \(\frac{63}{16}\)
- C \(\frac{3}{13}\)
- D \(\frac{13}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{16}{63}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \tan 2 \theta=\tan ((\theta+\phi)+(\theta-\phi))\left[\begin{array}{l}\because \tan (\theta+\phi)=\frac{4}{3} \\ \tan (\theta-\phi)=\frac{5}{12}\end{array}\right] \\ & =\frac{\tan (\theta+\phi)+\tan (\theta-\phi)}{1-\tan (\theta+\phi) \tan (\theta-\phi)} \\ &…
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