How do you solve $sin 2 x - cos x = 0$ $sin 2x - cos x = 0$ ?

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Answer 1 · 2016-06-10T02:42:50

Use the important double angle identity $sin 2 x = 2 sin x cos x$ $sin2x = 2sinxcosx$ to start the solving process.

$2 sin x cos x - cos x = 0$ $2sinxcosx - cosx = 0$

$cos x (2 sin x - 1) = 0$ $cosx(2sinx - 1) = 0$

$cos x = 0 or sin x = \frac{1}{2}$ $cosx= 0 or sinx = 1/2$

$90˚, 270˚, 30˚ and 150˚ or pi/2, (3pi)/2, pi/6 and (5pi)/6$

This can also be stated as $pi/2 + 2pin, (3pi)/2 + 2pin, pi/6 + 2pin and (5pi)/6 + 2pin$ , n being a natural number.

Hopefully the helps!

How do you solve sin 2x - cos x = 0sin2x−cosx=0 sin 2x - cos x = 0?