If your interval is , meaning your angle is measured in radians, why have you written your answer in degrees?
Dear friends,
The following is the question, I encountered:
What is the number of solutions for the pair of following equations
2 sin^{2}x - cos2x = 0
2 cos^{2}x - 3sinx = 0 _{ in the interval [0,2Pi] I added both the equations and I got 2sin2x - 3sinx +1 = 0 For which I thought the solution was 300, 900 and 1500 as the answers. But they say it is wrong?! Is it so? where I went wrong and what is the correct answer? could anyone help me. with warm regards, Aranga }
You can't add the two equations together and expect to retain the solutions to the original equations.
They are only simultaneous in the sense that you are looking for solutions common to both equations, (or at least that's what I'm assuming is required). In that case, solve the two separately.
To illustrate the first point, consider the equations and
They have, respectively, solutions and
Add them and you get which has the solution
Both 'original' solutions have been lost and a spurious one created.