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 168664 by cortano1 last updated on 15/Apr/22

{ ((8cos x−8sin x=3)),((55tan x+((55)/(tan x)) =?)) :}

$$\:\:\:\:\:\begin{cases}{\mathrm{8cos}\:{x}−\mathrm{8sin}\:{x}=\mathrm{3}}\\{\mathrm{55tan}\:{x}+\frac{\mathrm{55}}{\mathrm{tan}\:{x}}\:=?}\end{cases} \\ $$

Answered by greogoury55 last updated on 15/Apr/22

(8cos x−8sin x)^2 = 9 64−64sin 2x = 9 ⇒55 = 64sin 2x ⇒sin 2x= ((55)/(64)) ⇒55(((sin x)/(cos x)) +((cos x)/(sin x)))= ⇒55((2/(sin 2x)))= ((55×2)/((((55)/(64))))) = 128

$$\:\left(\mathrm{8cos}\:{x}−\mathrm{8sin}\:{x}\right)^{\mathrm{2}} \:=\:\mathrm{9} \\ $$$$\:\mathrm{64}−\mathrm{64sin}\:\mathrm{2}{x}\:=\:\mathrm{9} \\ $$$$\Rightarrow\mathrm{55}\:=\:\mathrm{64sin}\:\mathrm{2}{x} \\ $$$$\Rightarrow\mathrm{sin}\:\mathrm{2}{x}=\:\frac{\mathrm{55}}{\mathrm{64}} \\ $$$$\:\Rightarrow\mathrm{55}\left(\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}\:+\frac{\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}}\right)= \\ $$$$\Rightarrow\mathrm{55}\left(\frac{\mathrm{2}}{\mathrm{sin}\:\mathrm{2}{x}}\right)=\:\frac{\mathrm{55}×\mathrm{2}}{\left(\frac{\mathrm{55}}{\mathrm{64}}\right)}\:=\:\mathrm{128}\: \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com