JEE Main 2014MathematicsTrigonometric EquationsHardMCQ

JEE Main 2014 — Trigonometric Equations Question with Solution

JEE Main 2014 (09 Apr Online)

Question

The number of values of α in 0, 2π for which 2sin3α-7sin2α+7sinα=2, is :

Choose an option

Show full solutionCorrect option: A
Correct answer
A3

Step-by-step explanation

Given 2sin3 α-7sin2 α+7sin α=2

⇒2sin3 α-1-7 sin α sin α-1=0

⇒sin α-12sin2 α+sin α+1-7 sin α=0 ∵a3-b3=a-ba2+ab+b2

⇒sin α-12 sin2 α-5 sin α+2=0

⇒sin α-12 sin α-1sin α-2=0

 ∴ sin α=1, sin α=12, sin α≠2, ∵sinx∈-1,1 
Now, sin α=1 ⇒ α=π2  ∵ α∈0, 2π
sin α=12 ⇒ α=π6,  5π6  ∵ α ∈0,  2π

Hence, 3 values of α  in 0 ,  2 π .

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About this question

This is a previous-year question from JEE Main 2014, covering the Trigonometric Equations 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.