# math

posted by .

how would you solve for x:
(3)^.5sin(2x)-2cos(2x)+2sin^2(x)=1

• math -

took me awhile, but here it is ...

√3sin(2x) - 2cos(2x) = 1 - 2sin^2 x
√3sin(2x) - 2cos(2x) = cos(2x)
√3sin(2x) = 3cos(2x)
sin(2x)/cos(2x) = 3/√3
tan(2x) = 3/√3
2x = 60º or 240º
then x = 30º or 120º
or
x = pi/6 or x = 2pi/3

I checked both answers, they work

## Similar Questions

1. ### trig

find the exact solutions 2cos^2x+3sinx=0 the way it stands, that is a "nasty" question. Are you sure the second term isn't 2sin(2x) ?
2. ### Vector Calculus

Hello...i had a question. I would really appreciate it if someone could help me...tnx in advance! K my question is Find the T(t) , N(t), B(t) for r(t)=<2sint,2cost,t>; t=pie/4 ...which are normal vectors, binomial vector and …
3. ### Math - Solving Trig Equations

Solve each equation for 0 is less than and equal to "x" is less than and equal to 360 3sinx = 2cos^{2}x ----- I don't know how to solve this equation...this is what I have, but I don't know if I'm on the right track or not 3sinx = …
4. ### Math - Solving Trig Equations

What am I doing wrong? Equation: sin2x = 2cos2x Answers: 90 and 270 .... My Work: 2sin(x)cos(x) = 2cos(2x) sin(x) cos(x) = cos(2x) sin(x) cos(x) = 2cos^2(x) - 1 cos(x) (+/-)\sqrt{1 - cos^2(x)} = 2cos^2(x) - 1 cos^2(x)(1 - cos^2(x))
5. ### math

the problem is 2cos^2x + sinx-1=0 the directions are to "use an identity to solve each equation on the interval [0,2pi). This is what i've done so far: 2cos^2x+sinx-1=0 2cos^2x-1+sinx=0 cos2x + sinx =0 1 - 2sin^2x + sinx = 0 -2sin^2x+sinx-1=0 …
6. ### math

how would you find the angle to (3)^.5sin(2x)-2cos(2x)+2sin^2(x)=1 I know that you have to use the trig identities but then when i substitue the sin and cos(2x) in i don't know what to do. please help
7. ### math

need an aswer quich ok thiers two the find sin(2pi/3 -pi/4) using sum and difference identites and then tan 5pi/12 using the same identites
8. ### Math Trig

Find all solutions on the interval [0,2pi] for the following: 2sin^2(x)-5sin(x)=-3 cos^2(x)+sin(x)=1
9. ### trig identites

since sin2x+√3cos2x=2sin(2x+60) find the general solution for the equation sin2x+√3cosx=0 thank you
10. ### Math trig

Hello guys. I am just wondering if tan^2 A (tan squared A) = sin^2 A /cos^2A And 2tan A = 2sin A / 2cos A This has been bothering me when I have to simplify trig. Thanks in advance.

More Similar Questions