The maximum value of `5 sin theta+3 sin (theta + pi/3) + 3` is -

Options

A. `alpha = 2n pi+(pi)/(3), n epsilon I`
B. `alpha = 2n pi +-(2pi)/(3), n epsilon I`
C. `alpha epsilon [(pi)/(3), (2pi)/(3)]`
D. `alpha = n pi+(-1)^(n)(pi)/(3), n epsilon I`

Answer

A

Explanation

If for `theta epsilon R`, ……………
`(5+3soc alpha)sin theta-3sin alpha.cos theta+3`
`sqrt((5+3cos alpha)^(2)+9sin^(2)alpha)+3=10`
`implies cos alpha = (1)/(2)`