Find max value of 1/{\sin^2 \theta+3 \sin \theta \cos \theta+5 \cos^2 \theta}=?

SSC CGL Model Paper 3

Question : 61 of 100

Marks: +1, -0

Find max value of

1/{\sin^2 θ+3 \sin θ \cos θ+5 \cos^2 θ}=?

Solution:

({\sin^2 θ+3 \sin θ \cos θ+5 \cos^2 θ})

=1+3\sinθ\cosθ+4({1+\cos2θ}/2)

=3+3/2\sin2θ+2\cos2θ

=3-√{4+9/4}=3-5/2=1/2

⇒ max (exp) = 2

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