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Question Number 164434 by mathlove last updated on 17/Jan/22

Answered by TheSupreme last updated on 17/Jan/22

$$2f\left(sin\left(x\right)\right)-f\left(cos\left(x\right)\right)=3x$$$$2f\left(cos\left(x\right)\right)-f\left(sin\left(x\right)\right)=3(\frac{\pi }{2}-x)$$$$3f\left(sin\left(x\right)\right)=6x-3(\frac{\pi }{2}-x)$$$$f\left(sin\left(x\right)\right)=9x-\frac{3}{2}\pi$$$$f\left(t\right)=9arcsin\left(x\right)-\frac{3}{2}\pi +2k\pi$$$$f\left(tan\left(x\right)\right)=9arcsin\left(tan\left(x\right)\right)-\frac{3}{2}\pi +2k\pi$$$$f\left(sin\left(2x\right)\right)=8x-\frac{3}{2}\pi +2k\pi$$$$$$

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