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Question Number 201460 by hardmath last updated on 06/Dec/23

$$\mathrm{Find}\mathrm{the}\mathrm{smallest}\mathrm{positive}\mathrm{period}\mathrm{of}\mathrm{the}$$$$\mathrm{function}:$$$$\mathrm{y}=\mid \tan 2\mathrm{x}\mid +\mid \cot 2\mathrm{x}\mid$$

Answered by Mathspace last updated on 07/Dec/23

$$y\left(x\right)=\mid tan\left(2x\right)\mid +\frac{1}{\mid tan\left(2x\right)\mid }$$$$y(x+\frac{\pi }{2})=\mid tan\left(2(x+\frac{\pi }{2})\right)+\frac{1}{\mid tan\left(2(x+\frac{\pi }{2})\right)}$$$$=\mid tan(2x+\pi )\mid +\frac{1}{\mid tan(2x+\pi )\mid }$$$$=\mid tan\left(2x\right)\mid +\frac{1}{\mid tan\left(2x\right)\mid }$$$$=f\left(x\right)sothesmallperiodis$$$$T=\frac{\pi }{2}$$

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