JEE Main 2023MathematicsTrigonometric Ratios & IdentitiesEasyMCQ

JEE Main 2023 — Trigonometric Ratios & Identities Question with Solution

JEE Main 2023 (30 Jan Shift 1)

Question

If tan15°+1tan75°+1tan105°+tan195°=2a, then the value of a+1a is :

Choose an option

Show full solutionCorrect option: A
Correct answer
A4

Step-by-step explanation

Given:

2a=tan15°+1tan75°+1tan105°+tan195°

⇒2a=tan15°+1tan90°-15°+1tan90°+15°+tan180°+15°

⇒2a=tan15°+1cot15°-1cot15°+tan15°

⇒2a=2tan15°

⇒a=tan15°

⇒a=tan45°-30°

⇒a=1-131+13

⇒a=3-13+1

So,

a+1a=3-13+1+3+13-1

⇒a+1a=3-12+3+122

⇒a+1a=82=4

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About this question

This is a previous-year question from JEE Main 2023, 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.