JEE Main 2016MathematicsTrigonometric Ratios & IdentitiesEasyMCQ

JEE Main 2016 — Trigonometric Ratios & Identities Question with Solution

JEE Main 2016 (10 Apr Online)

Question

If A>0, B>0 and A+B=π6, then the minimum positive value of tan⁡A+tan⁡B is :

Choose an option

Show full solutionCorrect option: B
Correct answer
B4-23

Step-by-step explanation

tan⁡A+B=tan⁡A+tan⁡B1-tan⁡Atan⁡B

⇒ 13=y1-tan⁡A tan⁡B where y=tan⁡A+tan⁡B

⇒ tan⁡A.tan⁡B=1-3y

 and, also AM≥GM

⇒ tan⁡A+tan⁡B2 ≥ tan⁡Atan⁡B

⇒ y ≥21- 3y

⇒ y2 ≥4-43y≥0

⇒ y ≤ -23-4 or y ≥ -23+4

y ≤ -23-4, is not possible as tan⁡A+tan⁡B>0

Therefore, y ≥ -23+4

Hence, minimum positive value is 4-23.

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About this question

This is a previous-year question from JEE Main 2016, covering the Trigonometric Ratios & Identities chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.