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Category: Trigonometry

hence-show-that-i-1-cos4-sin4-tan2-ii-1-cos6-sin6-tan3-

Question Number 10917 by okhema last updated on 02/Mar/17 $${hence}\:{show}\:{that} \\ $$$$\left.{i}\right)\frac{\mathrm{1}−{cos}\mathrm{4}\theta}{{sin}\mathrm{4}\theta}={tan}\mathrm{2}\theta \\ $$$$\left.{ii}\right)\frac{\mathrm{1}−{cos}\mathrm{6}\theta}{{sin}\mathrm{6}\theta}={tan}\mathrm{3}\theta \\ $$ Answered by sandy_suhendra last updated on 02/Mar/17 $$\mathrm{we}\:\mathrm{use}\:\:\:\:\mathrm{cos}\:\mathrm{2}\theta=\mathrm{1}−\mathrm{2sin}^{\mathrm{2}} \theta\:\Rightarrow\:\mathrm{2sin}^{\mathrm{2}}…

solve-in-0-2pi-1-2sin3x-0-

Question Number 76439 by mathocean1 last updated on 27/Dec/19 $$\mathrm{solve}\:\mathrm{in}\:\left[\mathrm{0};\mathrm{2}\pi\left[\:\right.\right. \\ $$$$\mathrm{1}+\mathrm{2sin3}{x}\leqslant\mathrm{0} \\ $$ Answered by john santu last updated on 27/Dec/19 $${sin}\mathrm{3}{x}=−\frac{\mathrm{1}}{\mathrm{2}}.\rightarrow{x}=\left\{\mathrm{10}^{{o}} ,\mathrm{50}^{{o}} ,\mathrm{130}^{{o}}…

without-using-calculator-or-table-find-the-exact-value-of-sin-tan-1-1-2-

Question Number 10873 by Saham last updated on 28/Feb/17 $$\mathrm{without}\:\mathrm{using}\:\mathrm{calculator}\:\mathrm{or}\:\mathrm{table},\:\mathrm{find}\:\mathrm{the}\:\mathrm{exact}\:\mathrm{value}\:\mathrm{of}\:\:: \\ $$$$\mathrm{sin}\left[\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}}\right)\right] \\ $$ Answered by fariraihmudzengerere75@gmail.c last updated on 28/Feb/17 $${Answer}\:\:\:.\:\mathrm{sin}\:\left[\mathrm{tan}^{−\mathrm{1}} \left({x}\right)\right]={x}/\sqrt{\left(\mathrm{1}+\boldsymbol{\mathrm{x}}\frac{\mathrm{2}}{}\right)} \\…

given-that-sinA-12-13-and-sinB-4-5-where-A-and-B-are-acute-angles-find-cos-A-B-and-sin-A-B-

Question Number 10837 by okhema last updated on 27/Feb/17 $${given}\:{that}\:{sinA}=\frac{\mathrm{12}}{\mathrm{13}}{and}\:{sinB}=\frac{\mathrm{4}}{\mathrm{5}}, \\ $$$${where}\:{A}\:{and}\:{B}\:{are}\:{acute}\:{angles}, \\ $$$${find}\:{cos}\left({A}−{B}\right)\:{and}\:{sin}\left({A}+{B}\right) \\ $$$$ \\ $$ Answered by ridwan balatif last updated on…

Given-that-sin-x-sin-y-sin-cos-x-cos-y-cos-Show-that-cos-x-y-1-2-

Question Number 10825 by Saham last updated on 26/Feb/17 $$\mathrm{Given}\:\mathrm{that}\: \\ $$$$\mathrm{sin}\left(\mathrm{x}\right)\:−\:\mathrm{sin}\left(\mathrm{y}\right)\:=\:\mathrm{sin}\left(\theta\right) \\ $$$$\mathrm{cos}\left(\mathrm{x}\right)\:+\:\mathrm{cos}\left(\mathrm{y}\right)\:=\:\mathrm{cos}\left(\theta\right) \\ $$$$\mathrm{Show}\:\mathrm{that}\: \\ $$$$\mathrm{cos}\left(\mathrm{x}\:+\:\mathrm{y}\right)\:=\:−\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by mrW1 last updated…