Hi, y'all. I can't figure out what trig identities were used.
4cos2x = 8sinxcosx
4cos2x - 8sinxcosx = 0
Now I'm stuck. I know the answer is 4 - 4tan2x=0 but how what it done?
Thanks.
What exactly are you trying to do? The statement itself is NOT an identity, it's not true for x= 0. If you are asking for an identity that will help solve the equation? Then, yes, sin2x= 2 sin(x)cos(x) so 8sin(x)cos(x)= 4(2sin(x)cos(x))= 4sin 2x. So the equatioin can be written as 4 cos(2x)= 4 sin(2x). cos(2x)= sin(2x). Dividing both sides by cos(2x), sin(2x)/cos(2x)= tan(2x)= 1. tangent is equal to 1 when \(\displaystyle x= \pi/4\), \(\displaystyle x= -\pi/4\), and multiples of \(\displaystyle 2\pi\) added to that. So \(\displaystyle 2x= \frac{\pi}{4}+ 2n\pi\) and \(\displaystyle 2x= -\frac{\pi}{4}+ 2n\pi\) so that \(\displaystyle x= \frac{\pi}{8}+ n\pi\) and \(\displaystyle x= -\frac{\pi}{8}+ n\pi\).
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