JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
If \(\tan 15^{\circ}+\frac{1}{\tan 75^{\circ}}+\frac{1}{\tan 105^{\circ}}+\tan 195^{\circ}=2 a\), then the value of \(\left(a+\frac{1}{a}\right)\) is :
- A \(4\)
- B \(4-2 \sqrt{3}\)
- C \(2\)
- D \(5-\frac{3}{2} \sqrt{3}\)
Answer & Solution
Correct Answer
(A) \(4\)
Step-by-step Solution
Detailed explanation
\(\tan 15^{\circ}=2-\sqrt{3}\) \(\frac{1}{\tan 75^{\circ}}=\cot 75^{\circ}=2-\sqrt{3}\) \(\frac{1}{\tan 105^{\circ}}=\cot \left(105^{\circ}\right)=-\cot 75^{\circ}=\sqrt{3}-2\) \(\tan 195^{\circ}=\tan 15^{\circ}=2-\sqrt{3}\) \(2(2-\sqrt{3})=2 a \Rightarrow a =2-\sqrt{3}\)…
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