1. trig general solution

$\displaystyle cosx-sin3x=\sqrt2$
$\displaystyle 6cos^2x+8sinxcosx=0$

How can I solve this equation and find out the general solution.Please give me any idea.

2. Re: trig general solution

Originally Posted by srirahulan
$\displaystyle cosx-sin3x=\sqrt2$
$\displaystyle 6cos^2x+8sinxcosx=0$

How can I solve this equation and find out the general solution.Please give me any idea.
The second factorises very easily. Set each factor equal to 0.

3. Re: trig general solution

Ok Thanks,how can I solve first one?

4. Re: trig general solution

Write $\displaystyle cosx=sin(\frac{\pi}{2}-x)$ and use trigonometric transformation the equation becomes $\displaystyle cos(\frac{\pi}{4}+x)sin(\frac{\pi}{4}-2x)=\frac{1}{\sqrt{2}}$
Look for sign changes of this function in the interval $\displaystyle [0,2\pi]$ the roots are as shown in this link cos(pi/4+x)sin(pi/4 -2x) - 1/sqrt(2) - Wolfram|Alpha

5. Re: trig general solution

This is one of the best techniques to solving problems (not just mathematical by the way, but problems in general) and this is the first thing you should do any of these sorts of geometry problems. nike free running nike free running shoes for women nike free 3.0

6. Re: trig general solution

Or, you will get a cubic in Sin^2(x) or cos^2(x), solve it using Cubic function - Wikipedia, the free encyclopedia.

Salahuddin
Maths online