Question

Find the maximum value of `1+sin(pi/4+theta) + 2cos(pi/4-theta)`.
A. 1
B. 2
C. 3
D. 4

Answer 1

Correct Answer - 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`