1.

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

Answer»

1
2
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4

Solution :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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