Menu Close

Category: Trigonometry

sin-x-3cos-x-tan-x-3-True-or-false-

Question Number 12905 by 433 last updated on 06/May/17 $$\mathrm{sin}\:\left({x}\right)=\mathrm{3cos}\:\left({x}\right)\:\Leftrightarrow\mathrm{tan}\:\left({x}\right)=\mathrm{3} \\ $$$${True}\:{or}\:{false}? \\ $$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 06/May/17 $$\left.\mathrm{1}\right){false}\:{if}:\:{cosx}=\mathrm{0}\Rightarrow{x}=\mathrm{2}{k}\pi+\frac{\pi}{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right){true}\:{if}\:{x}\neq\mathrm{2}{k}\pi+\frac{\pi}{\mathrm{2}},{k}\in\boldsymbol{{Z}}\:. \\…

If-g-x-4cos-4-x-2cos-2x-1-2-cos-4x-x-7-1-7-then-tbe-value-of-g-g-100-is-equal-to-

Question Number 143959 by bobhans last updated on 20/Jun/21 $$\:\:\mathrm{If}\:\mathrm{g}\left(\mathrm{x}\right)=\left(\mathrm{4cos}\:^{\mathrm{4}} \mathrm{x}−\mathrm{2cos}\:\mathrm{2x}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{4x}−\mathrm{x}^{\mathrm{7}} \right)^{\frac{\mathrm{1}}{\mathrm{7}}} \\ $$$$\mathrm{then}\:\mathrm{tbe}\:\mathrm{value}\:\mathrm{of}\:\mathrm{g}\left(\mathrm{g}\left(\mathrm{100}\right)\right)\:\mathrm{is} \\ $$$$\mathrm{equal}\:\mathrm{to}\:… \\ $$ Answered by Olaf_Thorendsen last updated on 20/Jun/21…

Question-143958

Question Number 143958 by bobhans last updated on 20/Jun/21 Answered by bramlex last updated on 20/Jun/21 $$\Rightarrow\:\begin{cases}{\mathrm{sin}\:^{\mathrm{2}} \alpha+\mathrm{2sin}\:\alpha\mathrm{sin}\:\beta+\mathrm{sin}\:^{\mathrm{2}} \beta=\mathrm{9}{p}}\\{\mathrm{cos}\:^{\mathrm{2}} \alpha+\mathrm{2cos}\:\alpha\mathrm{cos}\:\beta+\mathrm{cos}\:^{\mathrm{2}} \beta=\mathrm{9}{q}}\end{cases} \\ $$$$\Leftrightarrow\mathrm{2}+\mathrm{2cos}\:\left(\alpha−\beta\right)=\mathrm{9}\left({p}+{q}\right)\: \\ $$$$\Leftrightarrow\:\mathrm{2cos}\:\left(\alpha−\beta\right)=\mathrm{9}\left({p}+{q}\right)−\mathrm{2}…

What-is-the-value-of-sin-1-sin-2pi-3-

Question Number 143923 by Sravanth last updated on 19/Jun/21 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left[\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}\left(\frac{\mathrm{2}\pi}{\mathrm{3}}\right)\right)\right]? \\ $$ Commented by mr W last updated on 19/Jun/21 $$\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}\left(\frac{\mathrm{2}\pi}{\mathrm{3}}\right)\right)=\frac{\pi}{\mathrm{3}} \\ $$…

If-cos-cos-m-and-cos-sin-n-then-prove-that-m-2-n-2-cos-2-n-2-

Question Number 143913 by Sravanth last updated on 19/Jun/21 $$\mathrm{If}\:\:\frac{\mathrm{cos}\:\alpha}{{cos}\:\beta}\:=\:\mathrm{m}\:\mathrm{and}\:\frac{\mathrm{cos}\:\alpha}{\mathrm{sin}\:\beta}\:=\:\mathrm{n}\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\left(\mathrm{m}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} \right)\mathrm{cos}^{\mathrm{2}} \beta\:=\:{n}^{\mathrm{2}} \\ $$ Answered by Ar Brandon last updated on 19/Jun/21…

Question-143897

Question Number 143897 by liberty last updated on 19/Jun/21 Answered by bobhans last updated on 19/Jun/21 $$\:\:\mathrm{sin}\:^{\mathrm{2}} \:\frac{\pi}{\mathrm{8}}+\mathrm{cos}\:^{\mathrm{2}} \:\frac{\pi}{\mathrm{8}}+\mathrm{cos}\:^{\mathrm{2}} \:\frac{\mathrm{5}\pi}{\mathrm{8}}+\mathrm{sin}\:^{\mathrm{2}} \:\frac{\mathrm{5}\pi}{\mathrm{8}}=\mathrm{2} \\ $$ Terms of…