Q16 of 30 Page 6

Prove that the function is an increasing function in .


Using sin2θ = 2sinθcosθ



Using cos2θ = 2cos2θ – 1





For the function to be increasing in should be positive in


Let us first find


Differentiating y with respect to θ




When θ is in is in [1, √2] hence will be in [1, 2] and will be in [2, 4] and finally will be in [1, 3] which is positive hence and hence f(x) is strictly increasing


Hence proved


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