Solution :
We have 1 + sin(π4+θ) + 2cos(π4–θ)
= 1 + 1sqrt2(cosθ+cosθ) + √2(cosθ+cosθ)
= 1 + (1√2+√2) + (cosθ+cosθ)
= 1 + (1√2+√2).√2cos(θ–pi4)
∴ Maximum Value = 1 + (1√2+√2).√2 = 4
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