giải phương trình sau: a) cos `(3x-pi/4)=-\sqrt{2}/2 ` b) `2sin^2x-1+cos3x=0`

a)

`cos (3x - \frac{\pi}{4}) = - \frac{\sqrt{2}}{2}`

`<=> cos (3x - \frac{\pi}{4}) = cos \frac{3\pi}{4}`

`<=> [(3x - \frac{\pi}{4} = \frac{3\pi}{4} + k.2\pi),(3x - \frac{\pi}{4} = - \frac{3\pi}{4} + k.2\pi):}` `(k in ZZ)`

`<=> [(3x = \pi + k.2\pi),(3x = - \frac{\pi}{2} + k.2\pi):}` `(k in ZZ)`

`<=> [(x = \frac{\pi}{3} + \frac{k.2\pi}{3}),(x = - \frac{\pi}{6} + \frac{k.2\pi}{3}):}` `(k in ZZ)`

Vậy _____________________________________________

b)

`2sin^{2} x - 1 + cos 3x = 0`

`<=> 2.(\frac{1 - cos 2x}{2}) - 1 + cos 3x = 0`

`<=> (1 - cos 2x) - 1 + cos 3x = 0`

`<=> cos 3x - cos 2x = 0`

`<=> cos 3x = cos 2x`

`<=> [(3x = 2x + k.2\pi),(3x = - 2x + k.2\pi):}` `(k in ZZ)`

`<=> [(x = k.2\pi),(5x = k.2\pi):}` `(k in ZZ)`

`<=> [(x = k.2\pi),(x = \frac{k.2\pi}{5}):}` `(k in ZZ)`

Vậy _________________________________________________

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