Category: Trigonometry

Question Number 155466 by cortano last updated on 01/Oct/21 $$\tan {}^2\left(\frac{\pi }{16}\right)+\tan {}^2\left(\frac{2\pi }{16}\right)+\dots +\tan {}^2\left(\frac{7\pi }{16}\right)=?$$ Commented by VIDDD last updated on 01/Oct/21 $$canushowusolution$$…

Question Number 89848 by 9933039645 last updated on 19/Apr/20 $$Q1.Ifsin\theta =\frac{3}{5}thenfindthevalueoftan\theta +cot\theta$$ Commented by mahdi last updated on 19/Apr/20 $$\pm \frac{25}{12}$$$$\sin \theta =\frac{3}{5}\Rightarrow \mid \cos \theta \mid =\sqrt{1-{\sin }^2\theta }=\frac{4}{5}$$$$\mathrm{tan}\theta=\frac{\mathrm{sin}\theta}{\mathrm{cos}\theta}=\pm\frac{\mathrm{3}}{\mathrm{4}}\:\:\:\:\:\:\mathrm{cot}\theta=\frac{\mathrm{1}}{\mathrm{tan}\theta}=\pm\frac{\mathrm{4}}{\mathrm{3}}…

Question Number 89662 by 974342176 last updated on 18/Apr/20 $$Giventhat\sin A=\frac{1}{2}and\sin C=\frac{\sqrt{3}}{2}withoutu$$$$usingcalculatorsolve$$$$a)\tan (A+C)$$$$b)cos(A-C)$$ Answered by TANMAY PANACEA. last updated on…

Question Number 89599 by 20000193 last updated on 18/Apr/20 Commented by john santu last updated on 18/Apr/20 $$4a)\tan (A+C)=\frac{\tan A+\tan C}{1-\tan A.\tan C}$$$$case\left(1\right)=\frac{\frac{1}{\sqrt{3}}+\sqrt{3}}{1-\frac{1}{\sqrt{3}}.\sqrt{3}}=\mathrm{\infty }\left(undefined\right)$$$$case\left(2\right)=\frac{\frac{1}{\sqrt{3}}-\sqrt{3}}{1+\frac{1}{\sqrt{3}}.\sqrt{3}}=\frac{-2}{2\sqrt{3}}=-\frac{1}{\sqrt{3}}$$$${case}\:\left(\mathrm{3}\right)\:=\:\frac{\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}+\sqrt{\mathrm{3}}}{\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}.\sqrt{\mathrm{3}}}\:=\:\frac{\mathrm{4}}{\mathrm{2}\sqrt{\mathrm{3}}}\:=\:\frac{\mathrm{2}}{\:\sqrt{\mathrm{3}}} \…

Question Number 89580 by jagoll last updated on 18/Apr/20 Answered by $@ty@m123lastupdatedon18/Apr/20$$\frac{BD}{\sin x}=\frac{AD}{\sin \{180-(x+84+42)\}}$$$\$\frac{BD}{\sin x}=\frac{AD}{\sin (54-x)}\dots \left(1\right)$$$$\frac{BD}{\sin 84}=\frac{BC}{\sin \{180-(84+42)\}}$$$$\frac{BD}{\sin 84}=\frac{AD}{\sin 54}\dots \left(2\right)$$$${From}\:\left(\mathrm{1}\right)\:\&\left(\mathrm{2}\right),…