COMEDK · Maths · 8. Trigonometric Ratios & Identities
\(\dfrac{\cos 9^{\circ}+\sin 9^{\circ}}{\cos 9^{\circ}-\sin 9^{\circ}}=\)
- A tan 18\(^\circ\)
- B tan 54\(^\circ\)
- C tan 36\(^\circ\)
- D tan 9\(^\circ\)
Answer & Solution
Correct Answer
(B) tan 54\(^\circ\)
Step-by-step Solution
Detailed explanation
Divide the numerator and the denominator by \(\cos 9^{\circ}\): \(\dfrac{\cos 9^{\circ} + \sin 9^{\circ}}{\cos 9^{\circ} - \sin 9^{\circ}} = \dfrac{1 + \tan 9^{\circ}}{1 - \tan 9^{\circ}}\) Using the identity \(\tan(A + B) = \dfrac{\tan A + \tan B}{1 - \tan A \tan B}\), and…
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