KVPY SX SB Exam 19-Nov-2017 Question Paper

Question : 16 of 120

Marks: +1, -0

The number of solutions of the equation sinθ + cosθ = sin2θ in the interval [–π, π] is

Solution:

Squaring

\sin^2θ + \cos^2θ + 2 \sin^ 2θ = \sin^22θ

⇒ \sin^22θ -\sin2θ -1 = 0

\sin2θ=({√5-1}/2,)\sin2θ ={√5+1}/2

(reject)
two solution exist between

=π/2\to\ -π/2\ &\ π/4

to 0 (2 solution)

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