Question

Please hurry its timed and i really need help!

Answer 1

Hello!:

Let's take this problem in steps:

`sinx-√(3-3sin^2(x))=0\\\\\text{We know that } sin^2(x) + cos^2(x)=1 \text{ and that } cos^2x=1-sin^2(x)\\\\sin(x)-√(3(1-sin^2(x)))=0\\\\sin(x)-√(3*cos^2(x))=0\\\\sin(x)-√(3)*cos(x)=0`

Now we need to find the value of sin(x) and cos(x) where the value becomes zero:

--> and it so happens to be:

`sin(30)=(1)/(2) \\\\cos(120)=(√(3))/(2)`

Thus:

`sin(30)-√(3)*cos(120)=0\\\\(1)/(2) -√(3)*(√(3) )/(2) =0\\\\\\(1)/(2) -(1)/(2) =0\\\\0=0`

Answer: (B)