Posted by **mike** on Sunday, May 3, 2009 at 9:11pm.

how would you solve for x:

(3)^.5sin(2x)-2cos(2x)+2sin^2(x)=1

using trig identites. please help

- math -
**Reiny**, Sunday, May 3, 2009 at 10:48pm
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

## Answer This Question

## Related Questions

- math - how would you find the angle to (3)^.5sin(2x)-2cos(2x)+2sin^2(x)=1 I know...
- math - the problem is 2cos^2x + sinx-1=0 the directions are to "use an identity ...
- Math - Solving Trig Equations - Solve each equation for 0 is less than and equal...
- Math Trig - Find all solutions on the interval [0,2pi] for the following: 2sin^2...
- trig - find the exact solutions 2cos^2x+3sinx=0 the way it stands, that is a "...
- Vector Calculus - Hello...i had a question. I would really appreciate it if ...
- math - need an aswer quich ok thiers two the find sin(2pi/3 -pi/4) using sum and...
- Math - Solving Trig Equations - What am I doing wrong? Equation: sin2x = 2cos2x ...
- trig identites - since sin2x+√3cos2x=2sin(2x+60) find the general solution...
- trig 30 - Please help I need to solve the following question for x, where 0<x...

More Related Questions