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Question: Answered & Verified by Expert
The value of $\tan 7 \frac{1}{2}^{\circ}$. is equal to
MathematicsTrigonometric Ratios & IdentitiesJEE Main
Options:
  • A $\sqrt{6}+\sqrt{3}+\sqrt{2}-2$
  • B $\sqrt{6}-\sqrt{3}+\sqrt{2}-2$
  • C $\sqrt{6}-\sqrt{3}+\sqrt{2}+2$
  • D $\sqrt{6}-\sqrt{3}-\sqrt{2}-2$
Solution:
1143 Upvotes Verified Answer
The correct answer is: $\sqrt{6}-\sqrt{3}+\sqrt{2}-2$
We have $\tan A=\frac{\sin A}{\cos A}=\frac{2 \sin A \cos A}{2 \cos ^2 A}=\frac{\sin 2 A}{1+\cos ^2 A}$
Putting
$A=7 \frac{1}{2}^{\circ} \Rightarrow \tan 7{\frac{1^{\circ}}{2}}^{\circ}=\frac{\sin 15^{\circ}}{1+\cos 15^{\circ}}$

On simplification, we get
$\tan 7 \frac{1}{2}^{\circ}=\sqrt{6}-\sqrt{3}+\sqrt{2}-2$

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