Solve the question: sin(2x)=cos(x), for values of x between 0 and 2 Pi

Answer 1

You'll find it very helpful to remember that sin(2x)=2sin(x)cos(x) here, since this means that you're trying to find all the solutions of 2sin(x)cos(x)=cos(x). These will be equal under two possible scenarios: firstly if cos(x)=0 (since both sides will be zero), and secondly if 2sin(x)=1, or sin(x)=0.5 (i.e. after you've cancelled out the cos(x) terms from both sides). Solve both of those equalities for all possible values between 0 and 2pi, and you've done it. I think you'll find there are four of them - two from each scenario.