Menu Close

Category: Trigonometry

Solve-1-cos-x-1-cos-x-2sin-x-

Question Number 134165 by liberty last updated on 28/Feb/21 $$\mathrm{Solve}\:\sqrt{\mathrm{1}+\mathrm{cos}\:\mathrm{x}}\:+\:\sqrt{\mathrm{1}−\mathrm{cos}\:\mathrm{x}}\:=\:\mathrm{2sin}\:\mathrm{x} \\ $$ Answered by EDWIN88 last updated on 28/Feb/21 $$\mathrm{square}\:\mathrm{both}\:\mathrm{sides} \\ $$$$\Leftrightarrow\:\mathrm{2}+\mathrm{2}\sqrt{\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}}\:=\:\mathrm{4sin}\:^{\mathrm{2}} \mathrm{x} \\…

sin-1-

Question Number 68482 by Maclaurin Stickker last updated on 11/Sep/19 $$\mathrm{sin}\:\mathrm{1}^{°} \:=\:? \\ $$ Commented by mr W last updated on 11/Sep/19 $$\mathrm{sin}\:\mathrm{1}^{°} \:=\:\mathrm{sin}\:\frac{\pi}{\mathrm{180}}\:\approx\frac{\pi}{\mathrm{180}}=\mathrm{0}.\mathrm{0174533} \\…

sin-1-3-5-tan-1-1-7-

Question Number 133976 by liberty last updated on 26/Feb/21 $$\:\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{3}}{\mathrm{5}}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{7}}\right)=? \\ $$ Answered by bemath last updated on 26/Feb/21 $$\mathrm{let}\:\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{3}}{\mathrm{5}}\right)=\vartheta\:\Rightarrow\begin{cases}{\mathrm{sin}\:\vartheta=\frac{\mathrm{3}}{\mathrm{5}}}\\{\mathrm{tan}\:\vartheta=\frac{\mathrm{3}}{\mathrm{4}}}\end{cases} \\ $$$$\Rightarrow\:\mathrm{sin}^{−\mathrm{1}}…

Question-68397

Question Number 68397 by Faradtimmy last updated on 10/Sep/19 Answered by $@ty@m123 last updated on 10/Sep/19 $$\left({a}\right)\:{LHS}=\sqrt{\mathrm{3}}\mathrm{cos}\:\theta−\mathrm{sin}\:\theta \\ $$$$=\mathrm{2}\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\mathrm{cos}\:\theta−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:\theta\right) \\ $$$$=\mathrm{2}\left(\mathrm{cos}\:\mathrm{30cos}\:\theta−\mathrm{sin}\:\mathrm{30sin}\:\theta\right) \\ $$$$=\mathrm{2cos}\:\left(\mathrm{30}+\theta\right) \\ $$$${Pl}.\:{check}\:{the}\:{question}.…

Question-68390

Question Number 68390 by TawaTawa last updated on 10/Sep/19 Answered by som(math1967) last updated on 10/Sep/19 $${tan}\left(\mathrm{2tan}^{−\mathrm{1}} \sqrt{\frac{\mathrm{2}{cos}^{\mathrm{2}} \frac{\theta}{\mathrm{2}}}{\mathrm{2}{sin}^{\mathrm{2}} \frac{\theta}{\mathrm{2}}}}\:\right)+{tan}\theta \\ $$$$={tan}\left\{\mathrm{2tan}^{−\mathrm{1}} \left(\mathrm{cot}\:\frac{\theta}{\mathrm{2}}\right)\right\}+\mathrm{tan}\:\theta \\ $$$$={tan}\left\{\mathrm{2tan}^{−\mathrm{1}}…