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Category: Trigonometry

Question-74520

Question Number 74520 by chess1 last updated on 25/Nov/19 Answered by MJS last updated on 26/Nov/19 $$\mathrm{0}\leqslant{x}<\mathrm{2}\pi \\ $$$$\mathrm{tan}\:{x}\:>\mathrm{sin}\:{x} \\ $$$$\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}>\mathrm{sin}\:{x} \\ $$$$\mathrm{case}\:\mathrm{1}:\:\mathrm{sin}\:{x}\:>\mathrm{0}\:\Leftrightarrow\:\mathrm{0}<{x}<\pi \\ $$$$\frac{\mathrm{1}}{\mathrm{cos}\:{x}}>\mathrm{1}\:\Leftrightarrow\:\mathrm{0}<{x}<\frac{\pi}{\mathrm{2}}\vee\frac{\mathrm{3}\pi}{\mathrm{2}}<{x}<\mathrm{2}\pi…

Question-8924

Question Number 8924 by tawakalitu last updated on 05/Nov/16 Commented by tawakalitu last updated on 05/Nov/16 $$\mathrm{From}\:\mathrm{the}\:\mathrm{diagram}\:\mathrm{above}\:,\:\mathrm{find}\:\mathrm{the}\:\mathrm{fraction} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{shaded}\:\mathrm{portion} \\ $$ Commented by Rasheed Soomro…

Question-8888

Question Number 8888 by 7C;00 last updated on 04/Nov/16 Commented by prakash jain last updated on 04/Nov/16 $$\mathrm{for}\:\mathrm{positive}\:\mathrm{numbers}: \\ $$$$\mathrm{Arithmetic}\:\mathrm{mean}\:\geqslant\:\mathrm{Harmonic}\:\mathrm{mean} \\ $$$$\mathrm{AM}=\frac{{a}_{\mathrm{1}} +{a}_{\mathrm{2}} +…+{a}_{{n}} }{{n}}=\frac{{n}}{{n}}=\mathrm{1}…

Question-8884

Question Number 8884 by tawakalitu last updated on 03/Nov/16 Answered by sandy_suhendra last updated on 04/Nov/16 Commented by sandy_suhendra last updated on 04/Nov/16 $$\mathrm{let}\:\mathrm{AL}=\mathrm{the}\:\mathrm{horizontal}\:\mathrm{distance}\:\mathrm{pointA}\:\mathrm{to}\:\mathrm{the}\:\mathrm{lower}\:\mathrm{hill} \\…

Question-8860

Question Number 8860 by MNG last updated on 02/Nov/16 Commented by ridwan balatif last updated on 02/Nov/16 $$\mathrm{2}.\:\mathrm{tanA}+\mathrm{cotA}=\mathrm{2cosec2A} \\ $$$$\:\:\:\:\:\:\frac{\mathrm{sinA}}{\mathrm{cosA}}+\frac{\mathrm{cosA}}{\mathrm{sinA}}=\mathrm{2cosec2A} \\ $$$$\:\:\:\:\:\frac{\mathrm{sin}^{\mathrm{2}} \mathrm{A}+\mathrm{cos}^{\mathrm{2}} \mathrm{A}}{\mathrm{sinA}×\mathrm{cosA}}=\mathrm{2cosec2A} \\…

If-tan-tan-a-tan-tan-then-show-that-sin-0-or-sin2-sin2-sin2-0-

Question Number 8859 by lepan last updated on 02/Nov/16 $${If}\:\frac{{tan}\left(\alpha+\beta−\gamma\right)}{{tan}\left({a}−\beta+\gamma\right)}=\frac{{tan}\gamma}{{tan}\beta}\:{then}\:{show} \\ $$$${that}\:{sin}\left(\beta−\gamma\right)=\mathrm{0}\:{or}\:{sin}\mathrm{2}\alpha+{sin}\mathrm{2}\beta+{sin}\mathrm{2}\Upsilon=\mathrm{0}. \\ $$ Answered by myintkhaing last updated on 03/Nov/16 Commented by myintkhaing last…