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Question Number 208075 by hardmath last updated on 04/Jun/24

$$\mathrm{Find}:\int \sin (2\mathrm{x}-\frac{\pi }{4})=?$$

Answered by TonyCWX08 last updated on 04/Jun/24

$$sin(2x-\frac{\pi }{4})$$$$=sin\left(2x\right)cos\left(\frac{\pi }{4}\right)-sin\left(\frac{\pi }{4}\right)cos\left(2x\right)$$$$=\frac{\sqrt{2}}{2}(sin\left(2x\right)-cos\left(2x\right))$$$$$$$$\frac{\sqrt{2}}{2}\int sin\left(2x\right)-cos\left(2x\right)dx$$$$=\frac{\sqrt{2}}{2}(-\frac{cos\left(2x\right)+sin\left(2x\right)}{2})+c$$$$=-\frac{\sqrt{2}(cos\left(x\right)+sin\left(x\right))}{4}+c$$

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