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The maximum value of 1+sin(pi/4+theta)+2...

The maximum value of `1+sin(pi/4+theta)+2cos(pi/4-theta)` for real values of `theta` is

Text Solution

Verified by Experts

The correct Answer is:
`1+sqrt(5)`
` 1 + sin (( pi )/(4) + theta) + 2sin ((pi)/(4) - theta) `
`=1+sin((pi)/(4)+theta)+2cos((pi)/(2)-((pi)/(4)-theta))`
`=1+sin((pi)/(4)+theta)+2cos((pi)/(4)+theta)`
Hecne, the maximum value is `1+sqrt(3)`.
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