JEE Main 2019MathematicsTrigonometric Ratios & IdentitiesEasyMCQ

JEE Main 2019 — Trigonometric Ratios & Identities Question with Solution

JEE Main 2019 (12 Jan Shift 1)

Question

The maximum value of 3cos⁡θ+5sin⁡θ-π6 for any real value of θ is :

Choose an option

Show full solutionCorrect option: A
Correct answer
A19

Step-by-step explanation

Given fθ=3cos⁡θ+5sin⁡θ-π6

⇒fθ=3cos⁡θ+5sin⁡θ·32-cos⁡θ·12

⇒fθ=532sin⁡θ+12cos⁡θ

Now using the concept acosx+bsinx+c ∈ c-a2+b2, c+a2+b2, we can write

Maximum value of fθ is 5322+122=754+14=19

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Trigonometric Ratios & Identities chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2019, 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.