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Question Number 82456 by liki last updated on 21/Feb/20

Commented by abdomathmax last updated on 21/Feb/20

$$cos\left(5x\right)=sin\left(4x\right)\iff cos\left(5x\right)=cos(\frac{\pi }{2}-4x)\Rightarrow$$$$5x=\frac{\pi }{2}-4x+2k\pi or5x=-\frac{\pi }{2}+4x+2k\pi \Rightarrow$$$$9x=\frac{\pi }{2}+2k\pi orx=-\frac{\pi }{2}+2k\pi (k\in Z)\Rightarrow$$$$x=\frac{\pi }{18}+\frac{2k\pi }{9}orx=-\frac{\pi }{2}+2k\pi$$$$S=\{\frac{\pi }{18}+\frac{2k\pi }{9},kϵZ\}\cup \{(2k-\frac{1}{2})\pi ,k\in Z\}$$

Commented by jagoll last updated on 21/Feb/20

$$\cos 5x=\sin (\frac{\pi }{2}-5x)$$$$\Rightarrow \sin (\frac{\pi }{2}-5x)=\sin 4x$$$$\left(1\right)\frac{\pi }{2}-5x+2k\pi =4x$$$$9x=\frac{\pi }{2}+2k\pi \Rightarrow x=\frac{\pi }{18}+\frac{2k\pi }{9}$$$$\left(2\right)\frac{\pi }{2}+5x=4x+2k\pi$$$$x=-\frac{\pi }{2}+2k\pi$$

Commented by liki last updated on 21/Feb/20

$$...thankyousir$$

Commented by liki last updated on 21/Feb/20

$$...thankyouverymuchsir.$$

Commented by liki last updated on 21/Feb/20

$$sorysirwhydidyouadd2\mathrm{\Pi }kforcase1\mathrm{\&}2$$

Commented by abdomathmax last updated on 21/Feb/20

$$mustadd2\pi kbecauseisaperiod..$$

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