The-number-of-solutions-of-sin-x-tan-x-in-0-4pi-is-are-

Question Number 16093 by Tinkutara last updated on 17/Jun/17

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of} \\ $$$$\mid\mathrm{sin}\:{x}\mid\:=\:\mathrm{tan}\:{x}\:\mathrm{in}\:\left[\mathrm{0},\:\mathrm{4}\pi\right]\:\mathrm{is}/\mathrm{are}? \\ $$

Commented by Tinkutara last updated on 17/Jun/17

$$\mathrm{My}\:\mathrm{answer}\:\mathrm{comes}\:\mathrm{out}\:\mathrm{to}\:\mathrm{be}\:\mathrm{5}\:\mathrm{but} \\ $$$$\mathrm{answer}\:\mathrm{in}\:\mathrm{book}\:\mathrm{is}\:\mathrm{6}.\:\mathrm{How}? \\ $$

Commented by prakash jain last updated on 17/Jun/17

$$\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}=\pm\mathrm{sin}\:{x} \\ $$$$\mathrm{sin}\:{x}\left(\mathrm{1}\mp\mathrm{cos}\:{x}\right)=\mathrm{0} \\ $$$$\mathrm{sin}\:{x}=\mathrm{0} \\ $$$$\mathrm{0},\pi,\mathrm{2}\pi,\mathrm{3}\pi,\mathrm{4}\pi \\ $$

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