QJEEM23Ma0d7e: JEE Main 2023 Mathematics - Class 11 JEEM23Ma0d7e Solution: If tan ⁡ 15 ∘ + 1 tan ⁡ 75 ∘ + 1 tan ⁡ 105 ∘ + tan ⁡ 195 ∘ = 2…

Question

Verified Solution • 2025–26 Session moderate

If $\tan 15^{\circ} + \frac{1}{\tan 75^{\circ}} + \frac{1}{\tan 105^{\circ}} + \tan 195^{\circ} = 2 a$ , then the value of $(a + \frac{1}{a})$ is :

Accepted Answer

$\tan 15^{\circ} + \tan 15^{\circ} - \tan 15^{\circ} + \tan 15^{\circ}$

$= 2 \tan 15^{\circ}$

$= 2 (2 - \sqrt{3}) = 2 a \Rightarrow a = 2 - \sqrt{3}$

$∴$ $\frac{1}{a} + a \Rightarrow (2 + \sqrt{3}) + (2 - \sqrt{3}) = 4$

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