find the maximum value of √3 cosθ-sinθ.???
You get a maximum when the derivative is zero.
-�ã3 sin ƒÆ -cos ƒÆ = 0
tan ƒÆ = -1/�ã3
Į = -30 degrees
�ã3 cosƒÆ-sinƒÆ = 3/2 + 1/2 = 2
check: If theta = -29 degrees,
�ã3 cosƒÆ-sinƒÆ = 1.5149 + 0.4848 = 1.9997
If theta = -31 degrees,
�ã3 cosƒÆ-sinƒÆ = 1.4847 + 0.5150 = 1.9997
So it looks like the maximum is 2.