1.

If `alpha, beta` are different values of `theta` satisfying the equation `5 cos theta-12 sin theta=11`. If the value of `sin (alpha + beta) =-(5k)/(169)` , then find the value of k.

Answer» given that, `5cos theta - 12sintheta= 11`
`(5/13)sin theta - (12/13)sin theta = 11/13`
`sin (phi- theta) = 11/13`
let `sin x = sin a`
we can say that `x=a or pi - a`
`phi- theta = alpha- phi or pi-(alpha- phi) `
`pi - (alpha- theta) = (beta- phi)`
`pi- alpha+ phi= beta - phi`
`pi+ phi + phi = alpha + beta`
`sin(pi + 2phi) = sin(alpha+ beta)`
`sin (alpha+beta) = - sin 2 phi = -2sinphicos phi`
`= -2*5/13* 12/13`
`sin (alpha+ beta)= -120/169`
`(-5k)/cancel(169) = -120/cancel(169)`
we get, `:. k = 24`


Discussion

No Comment Found

Related InterviewSolutions