JEE Main 2015MathematicsTrigonometric EquationsMediumMCQ

JEE Main 2015 — Trigonometric Equations Question with Solution

JEE Main 2015 (11 Apr Online)

Question

If cosα+cosβ=32 and sinα+sinβ=12 and θ is the arithmetic mean of α & β, then sin2θ+cos2θ is equal to:

Choose an option

Show full solutionCorrect option: B
Correct answer
B75

Step-by-step explanation

Given 
cos α + cos β = 32
sin α + sin β = 12
⇒2cos(α+β2)cos(α-β2)=32 ......(i) and

2sin⁡(α+β2)cos⁡(α-β2)=12 ....(ii)

Dividing (ii) and (i)

tan α + β2
∴  tan⁡θ =13

sin2θ+cos⁡2θ = 2tan⁡θ1+tan2⁡θ+ 1-tan2⁡θ1+tan2⁡θ=2131+19+1-191+19

= 23+89109=1410=75

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About this question

This is a previous-year question from JEE Main 2015, 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.