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Question

The general value of x satisfying the equation 3 sin x+cos x=3 is given by


A

x=nπ+(1)n π4+π3,nZ

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B

x=nπ+(1)n π3+π6,nZ

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C

x=nπ± π6,nZ

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D

x=nπ± π3,nZ

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Solution

The correct option is B

x=nπ+(1)n π3+π6,nZ


Given:3 sin x+cos x=3 ...(i)This equation is of the form a sinθ+b cosθ=c ,where a=3b=1 and c=3Let:a=r cos α and b=r sin αNow,r=a2+b2=(3)2+12=2 and tan α=batan α=13 α =π6On puting α =3=r cos α andb=1=r sin α in equation (i) ,we get:r cos α sin x+r sin α cos x=3r sin (x+α)=3 2 sin (x+α)=3 sin (x+α)=32 sin (x+α)=sinπ3 sin (x+π6)=sin π3 x=nπ+(1)n π3π6,nZ


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