AP EAMCET · Maths · Trigonometric Ratios & Identities
\(\frac{\tan 52^{\circ}-\tan 38^{\circ}}{\tan 14^{\circ}}=\)
- A 1
- B 2
- C \(2 \sqrt{3}\)
- D \(\frac{2}{\sqrt{3}}\)
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
\(\frac{\tan 52^{\circ}-\tan 38^{\circ}}{\tan 14^{\circ}} = \frac{\tan(52^{\circ}-38^{\circ})(1+\tan 52^{\circ}\tan 38^{\circ})}{\tan 14^{\circ}}\) \(= \frac{\tan 14^{\circ}(1+\tan 52^{\circ}\tan 38^{\circ})}{\tan 14^{\circ}}\) \(= 1+\tan 52^{\circ}\tan 38^{\circ}\)…
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