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Category: Trigonometry

find-the-solution-of-equation-cos-2x-sin-3-x-3-sin-x-

Question Number 112173 by bobhans last updated on 06/Sep/20 $$\:\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{equation}\: \\ $$$$\sqrt{\mathrm{cos}\:\mathrm{2x}−\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}+\mathrm{3}}\:=\:\mathrm{sin}\:\mathrm{x}\: \\ $$ Answered by john santu last updated on 06/Sep/20 $${since}\:\mathrm{sin}\:{x}\:\geqslant\:\mathrm{0}\:,\:{then}\: \\…

tan-10tan60-

Question Number 46636 by azharkhan250963@gmail.com last updated on 29/Oct/18 $$\mathrm{tan}\:\theta=\mathrm{10tan60}^{°} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 29/Oct/18 $${tan}\theta=\mathrm{10}×\sqrt{\mathrm{3}}\: \\ $$$${tan}\theta=\mathrm{10}×\mathrm{1}.\mathrm{732} \\ $$$$\theta={tan}^{−\mathrm{1}} \left(\mathrm{17}.\mathrm{32}\right)…

Question-177694

Question Number 177694 by cortano1 last updated on 08/Oct/22 Commented by Strengthenchen last updated on 08/Oct/22 $${as}\:{the}\:{picture}, \\ $$$$\frac{\mathrm{200}}{\mathrm{sin}\:{y}}=\frac{\mathrm{36}}{{sin}\:\mathrm{5}°}\rightarrow\mathrm{sin}\:{y}=\frac{\mathrm{sin}\:\mathrm{5}°×\mathrm{50}}{\mathrm{9}}\rightarrow\mathrm{cos}\:{y}=\sqrt{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} {y}} \\ $$$${x}^{\mathrm{2}} +\mathrm{36}^{\mathrm{2}} −\mathrm{72}{x}\mathrm{cos}\:{y}=\mathrm{200}^{\mathrm{2}} \rightarrow{x}=\frac{\mathrm{72cos}\:{y}\pm\sqrt{\left(\mathrm{72cos}\:{y}\right)^{\mathrm{2}}…

find-5-6-7sin-2-if-tan-0-2-

Question Number 112136 by weltr last updated on 06/Sep/20 $${find}\:\:\:\frac{\mathrm{5}}{\mathrm{6}+\mathrm{7sin}\:\mathrm{2}\beta}\:,\:\:\:{if}\:\:\:\mathrm{tan}\:\beta\:\:=\:\:\mathrm{0}.\mathrm{2} \\ $$ Answered by bemath last updated on 06/Sep/20 $$\mathrm{tan}\:\beta\:=\:\frac{\mathrm{1}}{\mathrm{5}}\:\rightarrow\begin{cases}{{if}\:\:\beta\:{in}\:{I}−\:{quadrant}\rightarrow\begin{cases}{\mathrm{sin}\:\beta=\frac{\mathrm{1}}{\:\sqrt{\mathrm{26}}}}\\{\mathrm{cos}\:\beta=\frac{\mathrm{5}}{\:\sqrt{\mathrm{26}}}}\end{cases}}\\{{if}\:\beta\:{in}\:{III}−{quadrant}\rightarrow\begin{cases}{\mathrm{sin}\:\beta=−\frac{\mathrm{1}}{\:\sqrt{\mathrm{26}}}}\\{\mathrm{cos}\:\beta=−\frac{\mathrm{5}}{\:\sqrt{\mathrm{26}}}}\end{cases}}\end{cases} \\ $$$$\Leftrightarrow\:\frac{\mathrm{5}}{\mathrm{6}+\mathrm{14sin}\:\beta\mathrm{cos}\:\beta}\:=\:\frac{\mathrm{5}}{\mathrm{6}+\mathrm{14}\left(\frac{\mathrm{5}}{\mathrm{26}}\right)} \\ $$$$=\:\frac{\mathrm{5}×\mathrm{26}}{\mathrm{6}×\mathrm{26}+\mathrm{70}}\:=\:\frac{\mathrm{65}}{\mathrm{78}+\mathrm{35}}\:=\:\frac{\mathrm{65}}{\mathrm{113}} \\…

show-that-If-a-2-b-2-c-2-are-in-A-P-the-cotA-cotB-cotC-are-also-in-A-P-

Question Number 46569 by scientist last updated on 28/Oct/18 $${show}\:{that}\:\:{If}\:{a}^{\mathrm{2}} ,{b}^{\mathrm{2}} ,{c}^{\mathrm{2}\:} \:{are}\:{in}\:{A}.{P}\:\:{the}\:{cotA},{cotB},{cotC}\:{are} \\ $$$${also}\:{in}\:{A}.{P} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 28/Oct/18 $$\frac{{sinA}}{{a}}=\frac{{sinB}}{{b}}=\frac{{sinc}}{{c}}={k}\left({say}\right)…

If-in-triangle-ABC-cosB-b-cosC-c-show-that-the-triangle-is-isosceles-

Question Number 46570 by scientist last updated on 28/Oct/18 $${If}\:{in}\:{triangle}\:{ABC}\:\:\:\frac{{cosB}}{{b}}\:=\frac{{cosC}}{{c}},\:{show}\:{that}\:{the} \\ $$$${triangle}\:{is}\:{isosceles} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 28/Oct/18 $$\frac{{sinA}}{{a}}=\frac{{sinB}}{{b}}=\frac{{sinC}}{{c}} \\ $$$$\frac{{cosB}}{{cosC}}=\frac{{sinB}}{{sinC}}=\frac{{b}}{{c}} \\…