JEE Main 2023MathematicsTrigonometric EquationsHardNumerical

JEE Main 2023 — Trigonometric Equations Question with Solution

JEE Main 2023 (24 Jan Shift 2)

Question

Let S=θ∈[0,2π): tanπcosθ+tanπsinθ=0, then ∑θ∈Ssin2θ+π4 is equal to

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Show full solutionCorrect answer: 2
Correct answer
2

Step-by-step explanation

Given:

S=θ∈[0,2π): tanπcosθ+tanπsinθ=0

So,

tanπcosθ+tanπsinθ=0

⇒tanπcosθ=-tanπsinθ

⇒tanπcosθ=tan-πsinθ

⇒πcosθ=nπ-πsinθ; n∈Z

⇒sinθ+cosθ=n

Now,

-2≤sinθ+cosθ≤2

⇒-2≤n≤2

But n∈Z, so n=-1, 0, 1

So,

θ∈0,π2,3π4,7π4,3π2,π

So,

∑θ∈Ssin2θ+π4=12+12+0+0+12+12=2

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About this question

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