Question Number 86111 by john santu last updated on 27/Mar/20 $$\mathrm{sin}\:\left(\frac{\mathrm{3}\pi}{\mathrm{2}}\mathrm{cos}\:{x}\right)\:=\:−\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Commented by jagoll last updated on 27/Mar/20 $$\Leftrightarrow\mathrm{sin}\:\left(\frac{\mathrm{3}\pi}{\mathrm{2}}\mathrm{cos}\:\mathrm{x}\right)\:=\:\mathrm{sin}\:\left(−\frac{\pi}{\mathrm{6}}\right) \\ $$$$\frac{\mathrm{3}\pi}{\mathrm{2}}\mathrm{cos}\:\mathrm{x}\:=\:−\frac{\pi}{\mathrm{6}}\:+\:\mathrm{2k}\pi \\ $$$$\mathrm{cos}\:\mathrm{x}\:=\:\frac{\mathrm{2}}{\mathrm{3}\pi}\:\left\{−\frac{\pi}{\mathrm{6}}+\mathrm{2k}\pi\right\}…
Question Number 20576 by gopikrishnan005@gmail.com last updated on 28/Aug/17 $${sec}\left({A}−\mathrm{3}\Pi/\mathrm{2}\right) \\ $$ Answered by Tinkutara last updated on 28/Aug/17 $$\mathrm{sec}\:\left(\frac{\mathrm{3}\pi}{\mathrm{2}}−{A}\right)=−\mathrm{cosec}\:{A} \\ $$ Terms of Service…
Question Number 20506 by Tinkutara last updated on 27/Aug/17 $${Simplify}: \\ $$$$\mathrm{cos}^{−\mathrm{1}} \:\left(\frac{\mathrm{sin}\:{x}\:+\:\mathrm{cos}\:{x}}{\:\sqrt{\mathrm{2}}}\right),\:\frac{\pi}{\mathrm{4}}\:<\:{x}\:<\:\frac{\mathrm{5}\pi}{\mathrm{4}} \\ $$ Answered by ajfour last updated on 27/Aug/17 $$\:\theta=\mathrm{cos}^{−\mathrm{1}} \left[\mathrm{cos}\:\left(\pi/\mathrm{4}\right)\mathrm{cos}\:{x}+\mathrm{sin}\:\left(\pi/\mathrm{4}\right)\mathrm{sin}\:{x}\right] \\…
Question Number 20509 by Tinkutara last updated on 27/Aug/17 $${Simplify}: \\ $$$$\mathrm{cos}^{−\mathrm{1}} \:\left(\frac{\mathrm{sin}\:{x}\:+\:\mathrm{cos}\:{x}}{\:\sqrt{\mathrm{2}}}\right),\:\frac{\mathrm{5}\pi}{\mathrm{4}}\:<\:{x}\:<\:\frac{\mathrm{9}\pi}{\mathrm{4}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 20505 by Tinkutara last updated on 27/Aug/17 $${Simplify}: \\ $$$$\mathrm{cos}^{−\mathrm{1}} \:\left(\frac{\mathrm{3}}{\mathrm{5}}\:\mathrm{cos}\:{x}\:+\:\frac{\mathrm{4}}{\mathrm{5}}\:\mathrm{sin}\:{x}\right),\:{where} \\ $$$$−\frac{\mathrm{3}\pi}{\mathrm{4}}\:\leqslant\:{x}\:\leqslant\:\frac{\pi}{\mathrm{4}} \\ $$ Answered by ajfour last updated on 27/Aug/17 $${let}\:\mathrm{tan}\:\alpha=\frac{\mathrm{4}}{\mathrm{3}}\:\Rightarrow\:\mathrm{sin}\:\alpha=\frac{\mathrm{4}}{\mathrm{5}},…
Question Number 151493 by iloveisrael last updated on 21/Aug/21 $$\:\:\:\frac{\mathrm{cos}\:\left(\frac{\mathrm{5}\pi}{\mathrm{2}}−\mathrm{6}{x}\right)+\mathrm{sin}\:\left(\pi+\mathrm{4}{x}\right)+\mathrm{sin}\:\left(\mathrm{3}\pi−{x}\right)}{\mathrm{sin}\:\left(\frac{\mathrm{5}\pi}{\mathrm{2}}+\mathrm{6}{x}\right)+\mathrm{cos}\:\left(\mathrm{4}{x}−\mathrm{2}\pi\right)+\mathrm{cos}\:\left({x}+\mathrm{2}\pi\right)}\:=? \\ $$ Commented by MJS_new last updated on 21/Aug/21 $$\mathrm{tan}\:{x} \\ $$ Commented by liberty…
Question Number 20366 by ajfour last updated on 26/Aug/17 $$\mathrm{tan}\:^{\mathrm{2}} {x}+\mathrm{2tan}\:{x}\:\left(\mathrm{sin}\:{y}+\mathrm{cos}\:{y}\right)+\mathrm{2}=\mathrm{0} \\ $$$${Find}\:{x},{y}\:. \\ $$ Answered by mrW1 last updated on 26/Aug/17 $$\mathrm{D}=\mathrm{4}\left(\mathrm{sin}\:\mathrm{y}+\mathrm{cos}\:\mathrm{y}\right)^{\mathrm{2}} −\mathrm{4}×\mathrm{2}\geqslant\mathrm{0} \\…
Question Number 85845 by jagoll last updated on 25/Mar/20 $$\mathrm{solve}\:\mathrm{tanh}\:\left(\mathrm{x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{cosh}\:\left(\mathrm{x}\right)} \\ $$ Answered by MJS last updated on 25/Mar/20 $$\frac{\mathrm{sinh}\:{x}}{\mathrm{cosh}\:{x}}=\frac{\mathrm{1}}{\mathrm{cosh}\:{x}} \\ $$$$\mathrm{cosh}\:{x}\:\neq\mathrm{0}\:\forall{x}\in\mathbb{R} \\ $$$$\mathrm{cosh}\:{x}\:\neq\mathrm{0}\:\Rightarrow\:{x}\neq\left(\frac{\mathrm{2}{n}+\mathrm{1}}{\mathrm{2}}\right)\pi\mathrm{i} \\…
Question Number 20198 by Joel577 last updated on 24/Aug/17 $$\mathrm{Find}\:\mathrm{exact}\:\mathrm{form}\:\mathrm{of} \\ $$$$\mathrm{cos}\:\left(\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}}\right)\right) \\ $$ Answered by Tinkutara last updated on 24/Aug/17 $$\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}}\right)\:=\:\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{2}}{\:\sqrt{\mathrm{5}}}\right)…
Question Number 20091 by Tinkutara last updated on 21/Aug/17 $$\mathrm{Prove}\:\mathrm{that}\:\underset{{n}=\mathrm{0}} {\overset{\mathrm{3}} {\sum}}\mathrm{tan}^{\mathrm{2}} \:\frac{\left(\mathrm{2}{n}\:+\:\mathrm{1}\right)\pi}{\mathrm{16}}\:=\:\mathrm{28}. \\ $$ Answered by ajfour last updated on 21/Aug/17 $$\frac{\mathrm{sin}\:^{\mathrm{2}} {A}}{\mathrm{cos}\:^{\mathrm{2}} {A}}+\frac{\mathrm{sin}\:^{\mathrm{2}}…