1.

If `max{5sin theta+3sin(theta-alpha)}=7` then the set of possible vaues of `alpha` is `theta in R`

Answer» `5 sin theta + 3 sin( theta - alpha)`
`= ( 5 + 3 cos alpha) sin theta - 3sin alpha cos theta`
`= {(5 + 3cos alpha)^2 + 9 sin^2 alpha}`
`= sqrt((5+ 3 cos alpha)^2 + 9 sin^2 alpha) sin(theta - phi) `
`max{5sin theta + 3 cos(theta- alpha)} `
`= sqrt((5+3cos alpha)^2 + 9sin^2alpha)`
=`7`
`25 + 30 cos alp-ha + 9 = 49`
`30 cos alpha = 15`
`cos alpha = 1/2`
`alpha = 2n pi + - pi/3`
option A is correct
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