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the number of values of x satisfying the equation √3 cos x + sin x = 1 in the interval [ 0, pi] i got that sin ( 60 + x) = sin(30) but i didn’t get how the soltuion for this question is 4

the number of values of x satisfying the equation √3 cos x + sin x = 1 in the interval [ 0, pi]
i got that sin ( 60 + x) = sin(30)
but i didn’t get how the soltuion for this question is 4

Grade:11

1 Answers

8279954633
15 Points
5 years ago
It is basically a quadratic equation in sinxconsider sinx=t so the equation reduces to2t^2+5t-3=0Which implies2t^2+6t-t-3=0On further equating (factorising)2t(t+3)-(t+3)=0So (t+3)(2t-1)=0 noweither t+3=0=>t=-3(impossible as t=sinx and -1t=½=>sinx=½=>x=π/6,5π/6,13π/6,17π/6 (0,3π)

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