Find `theta` for which the expression `sin(theta+pi/6)+cos(theta+pi/6)` attains maximum value

Find the value of theta varepsilon(0,2 pi) for which sin(theta+(pi)/(6))+cos(theta+(pi)/(6)) is maximum:

For theta in(0,pi/2) , the maximum value of sin(theta+pi/6)+cos(theta+pi/6) is attained at theta =

For theta in(0,pi/2) , the maximum value of sin(theta+pi/6)+cos(theta+pi/6) is attained at theta =

Find the value of theta for which sin theta sin(theta - pi/3 ) is maximum.

The maximum value of the expression sin theta cos^(2)theta(AA theta in [0, pi]) is

The maximum value of the expression sin theta cos^(2)theta(AA theta in [0, pi]) is

If 2 sin(theta+(pi)/(3))=cos(theta-(pi)/(6)) , then tantheta =

The value of theta in the range 0 lt= theta lt= (pi)/(2) which satisfies the equation sin ( theta +(pi)/(6)) = cos theta is equal to

The value of the expression sin^6 theta + cos^6 theta + 3 sin^2 theta. cos^2 theta equals

For theta in(0,(pi)/(2)), the maximum value of sin(theta+(pi)/(6))+cos(theta+(pi)/(6)) is attained at theta=