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Find the maximum value of 1+sin((pi)/(4)...

Find the maximum value of `1+sin((pi)/(4)+theta)+2cos((pi)/(4)-theta)`

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
d
We have , `1+sin(pi/4+theta)+2cos(pi/4-theta)`
`=1+1/sqrt(2)(costheta+sintheta) + sqrt(2)(costheta+sintheta) = 1+1/sqrt(2(+sqrt(2))(costheta+sintheta)`
`=1+(1/sqrt(2)+sqrt(2)).sqrtcos(theta-pi/4)`
`therefore` maximum value`=1+(1/sqrt(2)+sqrt(2)).sqrt(2)=4`
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