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Question Number 7900 by tawakalitu last updated on 23/Sep/16

$$Findanequationofthetangentlinetothecurve$$$$y={tan}^{2}xatthepoint(\frac{\pi }{3},3)$$

Commented by sou1618 last updated on 24/Sep/16

$$l:tangentline$$$$3={tan}^2\left(\frac{\pi }{3}\right)$$$$sopoint(\pi /3,3)isonl$$$$$$$$y{}^{\prime }=2tan\left(x\right)\cdot {\left(tanx\right)}^{\prime }$$$$y{}^{\prime }=2tan\left(x\right)\cdot \frac{1}{{cos}^{2}x}$$$$l:y-3=2tan\left(\pi /3\right)\cdot \frac{1}{{cos}^2\left(\pi /3\right)}(x-\pi /3)$$$$l:y=2\sqrt{3}\cdot 4(x-\pi /3)+3$$$$l:y=8\sqrt{3}x+3-\frac{8\pi \sqrt{3}}{3}$$$$l:y=8\sqrt{3}x+3-\frac{8\pi }{\sqrt{3}}.$$$$$$

Commented by tawakalitu last updated on 24/Sep/16

$$Thankyousomuch.$$

Answered by prakash jain last updated on 02/Oct/16

$$\mathrm{see}\mathrm{comments}$$

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