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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

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
D
we have `1+((pi)/(4)+theta)+2cos ((pi)/(4)-theta)`
`=1+(1)/sqrt(2)(cos theta+sin theta)+sqrt(2)(cos theta+sin theta)=1+((1)/sqrt(2)+sqrt(2))(cos theta+sin theta)`
`=1+((1)/sqrt(2)+sqrt(2)).sqrt(2)cos(theta-(pi)/(4))`
`therefore` maximum value `1+((1)/sqrt(2)+sqrt(2)).sqrt(2)=4`.
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