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MakcuM [25]
3 years ago
10

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

Mathematics
1 answer:
Sati [7]3 years ago
8 0

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

<h2>✓(sinx)2 = ✓0.25</h2>

<h2>sinx=0.5</h2><h2> </h2><h2>x=sin^-(0.5)</h2>

<h2>x=30°</h2>

<h3>check quadrant where sin is positive, sin is +ve in second quandrant</h3>

180-x= Theta(X)

180-30=X

X=150°

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

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