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Find the maximum value of 1 + sin(π4+θ) + 2cos(π4θ)

Solution :

We have 1 + sin(π4+θ) + 2cos(π4θ)

= 1 + 1sqrt2(cosθ+cosθ) + 2(cosθ+cosθ)

= 1 + (12+2) + (cosθ+cosθ)

= 1 + (12+2).2cos(θpi4)

   Maximum Value = 1 + (12+2).2 = 4


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