SOLUTION: Hi Please can you help me find the general solution in radians of the equation {{{sin2x

Click here to see ALL problems on Trigonometry-basics

Question 27039: Hi
Please can you help me find the general solution in radians of the equation

Thank you very much
Answer by kev82(151) (Show Source):
You can put this solution on YOUR website!
Hi,
There is probably a trig identity that solves this immediatly, but I'm useless at remembering them, I only know 3 or 4 myself. So I looked for a cleverer solution. And after staring for a few minutes, I found it.
Square your equation, and see what you get.

Now using, , and subtracting one from both sides, we get the much nicer

This can be solved either by using the sine addition formula and saying that or by saying that either or . Either way you should get the solutions as

'Wait! Zero isn't a solution' I hear you shout. This is true, but think back to when we squared the equation. We have also solved because it squares to the same thing. So you have to check which solutions satisfy your original equation and then you're done.
Hope that helps. (If you do find an easier way to solve it I would be interested to know)
Kev

SOLUTION: Hi Please can you help me find the general solution in radians of the equation {{{sin2x - 1 = cos2x}}} Thank you very much