Question

Find all solutions of sin x - sqrt(1 - 3sin^2 x) = 0

Answer 1

sinx-✓(1-3sin2x)=0

-✓(1-3sin2x)=-sinx

apply squared both sides

(-✓(1-3sin2x)^2=(-sinx)^2

1-3sin2x=sin2x

collect like terms

-3sin2x-sin2x+1=0

-4sin2x+1=0

-4sin2x=-1

devide both sides by -4

sin2x=-1/-4

sin2x=0.25

sinx*sinx =0.25

[sinx]^2 = 0.25

apply square root both sides

✓(sinx)2 = ✓0.25

sinx=0.5

x=sin^-(0.5)

x=30°

check quadrant where sin is positive, sin is +ve in second quandrant

180-x= Theta(X)

180-30=X

X=150°

therefore, all angles for sinx -✓(1-3sin2x)=0 are (X= 30° and 150°)