Category: Trigonometry

Question Number 128780 by bramlexs22 last updated on 10/Jan/21 $$\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{x}\mathrm{from}\mathrm{the}\mathrm{equation}$$$$1+\sin \mathrm{x}+\sin {}^2\mathrm{x}+\sin {}^3\mathrm{x}+\sin {}^4\mathrm{x}+\dots +\mathrm{\infty }=4+2\sqrt{3}$$ Answered by liberty last updated on 10/Jan/21 $$\:\mathrm{Its}\:\mathrm{GP}\:\mathrm{with}\:\begin{cases}{\mathrm{T}_{\mathrm{1}}…

Question Number 128753 by bramlexs22 last updated on 10/Jan/21 $$\mathrm{Find}\mathrm{maximum}\mathrm{and}\mathrm{minimum}$$$$\mathrm{value}\mathrm{of}\mathrm{function}\mathrm{f}\left(\mathrm{x}\right)={27}^{\cos 2\mathrm{x}}.{81}^{\sin 2\mathrm{x}}?$$ Answered by liberty last updated on 10/Jan/21 $$\:\Leftrightarrow\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{3}^{\mathrm{3cos}\:\mathrm{2x}} .\:\mathrm{3}^{\mathrm{4sin}\:\mathrm{2x}}…

Question Number 128681 by bemath last updated on 09/Jan/21 $$\mathrm{Given}\sqrt[3]{\sin \mathrm{x}}-\sqrt[3]{\cos \mathrm{x}}=\frac{1}{\sqrt[3]{3}}$$$$\mathrm{then}\sin {}^2\mathrm{x}=?$$ Commented by MJS_new last updated on 09/Jan/21 $$\mathrm{not}\mathrm{funny}\mathrm{to}\mathrm{solve}\mathrm{exactly}\mathrm{but}\mathrm{possible}\dots$$…

Question Number 128645 by john_santu last updated on 09/Jan/21 $$\mathrm{If}6\tan {}^2\mathrm{x}+\tan \mathrm{x}.\sec \mathrm{x}=\sec {}^2\mathrm{x}\mathrm{where}$$$$\frac{\pi }{2}<\mathrm{x}<\frac{3\pi }{2}\mathrm{has}\mathrm{the}\mathrm{roots}{\mathrm{x}}_1\mathrm{and}{\mathrm{x}}_2.\mathrm{Find}$$$$\mathrm{the}\mathrm{value}\mathrm{of}\sin ({\mathrm{x}}_1+{\mathrm{x}}_2).$$ Answered by liberty…

Question Number 128643 by liberty last updated on 09/Jan/21 $$\mathrm{If}\tan \mathrm{x}+\sec \mathrm{x}=\mathrm{b}\mathrm{then}\cos \mathrm{x}=?$$ Commented by john_santu last updated on 09/Jan/21 $$\tan \mathrm{x}=\mathrm{b}-\sec \mathrm{x}$$$$\mathrm{squaring}\:\Rightarrow\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}=\mathrm{b}^{\mathrm{2}} −\mathrm{2bsec}\:\mathrm{x}+\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}…