Question and Answers Forum

All Questions      Topic List

Trigonometry Questions

Previous in All Question      Next in All Question      

Previous in Trigonometry      Next in Trigonometry      

Question Number 103643 by bemath last updated on 16/Jul/20

$$if\sin x+\cos x=\frac{5}{6}$$$$then\frac{1}{\sin x}+\frac{1}{\cos x}?$$

Answered by Dwaipayan Shikari last updated on 16/Jul/20

$${(sinx+cosx)}^2-2sinxcosx=1$$$$\frac{25}{36}-2sinxcosx=1$$$$sinxcosx=-\frac{11}{72}$$$$\frac{1}{sinx}+\frac{1}{cosx}=\frac{\frac{5}{6}}{\frac{-11}{72}}=-\frac{60}{11}$$

Answered by bobhans last updated on 16/Jul/20

$$\frac{1}{\sin x}+\frac{1}{\cos x}=p...\left(2\right)$$$$\left(1\right)\times \left(2\right)\Rightarrow (\sin x+\cos x)$$$$(\frac{1}{\sin x}+\frac{1}{\cos x})=\frac{5p}{6}$$$$\Rightarrow 1+\frac{\sin x}{\cos x}+\frac{\cos x}{\sin x}+1=\frac{5p}{6}$$$$\frac{1}{\cos x\sin x}+2=\frac{5p}{6}...\left(3\right)$$$${(\sin x+\cos x)}^2=\frac{25}{36}$$$$2\sin x\cos x=-\frac{11}{36}\Rightarrow \sin x\cos x=-\frac{11}{72}$$$$noweq\left(3\right)\Rightarrow -\frac{72}{11}+2=\frac{5p}{6}$$$$\frac{5p}{6}=-\frac{50}{11}\Rightarrow p=-\frac{60}{11}★$$

Answered by mathmax by abdo last updated on 16/Jul/20

$$\mathrm{sinx}+\mathrm{cosx}=\frac{5}{6}\Rightarrow {(\mathrm{sinx}+\mathrm{cosx})}^2=\frac{25}{36}\Rightarrow 1+2\mathrm{sinx}\mathrm{cosx}=\frac{25}{36}\Rightarrow$$$$2\mathrm{sinx}\mathrm{cosx}=\frac{25}{36}-1=-\frac{11}{36}\Rightarrow \mathrm{sinx}\mathrm{cosx}=-\frac{11}{72}\Rightarrow$$$$\frac{1}{\mathrm{sinx}}+\frac{1}{\mathrm{cosx}}=\frac{\mathrm{cosx}+\mathrm{sinx}}{\mathrm{sinx}\mathrm{cosx}}=\frac{\frac{5}{6}}{-\frac{11}{72}}=-\frac{5}{6}\times \frac{72}{11}=-\frac{5.24.3}{2.3.11}=-\frac{5.12}{11}=-\frac{60}{11}$$$$$$

Answered by Aziztisffola last updated on 16/Jul/20

$$\frac{1}{\sin x}+\frac{1}{\cos x}=\frac{\frac{5}{6}}{\sin \mathrm{x}.\cos \mathrm{x}}$$$${(\mathrm{cosx}+\mathrm{sinx})}^2=1+2\mathrm{sinxcosx}=\frac{25}{36}$$$$\mathrm{sinxcosx}=\frac{\frac{25}{36}-1}{2}=\frac{-\frac{11}{36}}{2}=-\frac{11}{72}$$$$\frac{1}{\sin x}+\frac{1}{\cos x}=\frac{\frac{5}{6}}{-\frac{11}{72}}=\frac{5}{6}\times \frac{72}{-11}=-\frac{360}{66}$$$$$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com