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Question Number 46534 by peter frank last updated on 28/Oct/18

$$\mathrm{using}\mathrm{taylors}\mathrm{expansion}$$$$\mathrm{find}\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}$$$$\mathrm{a})\tan 45°1^{\prime }$$$$\mathrm{b})\sin 30°1^{\prime }$$

Answered by tanmay.chaudhury50@gmail.com last updated on 28/Oct/18

$$a)y=f\left(x\right)whenxchangestox+△x$$$$ychangestoy+△y$$$$heref\left(x\right)=tanx$$$$y=tanx\frac{dy}{dx}={sec}^{2}x$$$$\frac{dy}{dx}=\frac{△y}{△x}$$$$△y=\frac{dy}{dx}△x$$$$△y={sec}^{2}x.△x$$$$△x=1^{{}^{\prime }}={\left(\frac{1}{60}\right)}^o=\frac{\pi }{180}\times \frac{1}{60}=0.00029$$$$△y={sec}^2{45}^o\times 0.00029=0.00058$$$$sovalueoftan\left({45}^o{1}^{\prime }\right)=1+0.00058=1.00058$$$$$$$$b)△y=\frac{dy}{dx}△x$$$$y=sinx\frac{dy}{dx}=cosx$$$$△y=cosx.△x$$$$△y=cos{30}^o\times 0.00029=\frac{\sqrt{3}}{2}\times 0.00029=0.00025$$$$sosin\left({30}^o{1}^{\prime }\right)=0.5+0.00025=0.50025$$

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