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Question Number 143993 Answers: 1 Comments: 0
Question Number 143987 Answers: 1 Comments: 0
$${If}\:{f}\left({x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{6}\right)+{f}\left({x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{4}\right)=\mathrm{2}{x} \\ $$$$\forall{x}\in{R}\:{th}\mathrm{e}{n}\:{f}\left(−\mathrm{3}\right)+{f}\left(\mathrm{9}\right)−\mathrm{5}{f}\left(\mathrm{1}\right)=? \\ $$
Question Number 143980 Answers: 1 Comments: 0
Question Number 143979 Answers: 1 Comments: 0
Question Number 143970 Answers: 1 Comments: 0
$$\mathrm{Given}\:\mathrm{that}\:\omega\:\mathrm{is}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{number}, \\ $$$$\omega^{\mathrm{7}} =\mathrm{1},\:\omega\neq\mathrm{1},\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\omega^{\mathrm{1}} +\omega^{\mathrm{2}} +\omega^{\mathrm{3}} +\omega^{\mathrm{4}} +\omega^{\mathrm{5}} +\omega^{\mathrm{6}} . \\ $$
Question Number 143965 Answers: 1 Comments: 1
Question Number 143964 Answers: 1 Comments: 2
$${x}_{\mathrm{1}} \:{and}\:\:{x}_{\mathrm{2}} \:\:{are}\:\:{solutions}\:\:{of}\:\:{equality}\:: \\ $$$$\:\:\mathrm{cos}\:\left(\frac{\pi{x}+\pi}{\mathrm{6}}\right)\:−\:\mathrm{sin}\:\left(\frac{\pi{x}−\pi}{\mathrm{6}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:\sqrt{\mathrm{3}}\:\:\:,\:\:\:\mathrm{0}\:\leqslant\:{x}\:\leqslant\:\mathrm{12} \\ $$$${Find}\:\:{the}\:\:{value}\:\:{of}\:\:{x}_{\mathrm{1}} +\:{x}_{\mathrm{2}} \:. \\ $$
Question Number 143963 Answers: 1 Comments: 0
$$\mathrm{A}=\mathrm{x}^{\mathrm{ln}\frac{\mathrm{y}}{\mathrm{x}}} .\mathrm{y}^{\mathrm{ln}\frac{\mathrm{z}}{\mathrm{x}}} .\mathrm{z}^{\mathrm{ln}\frac{\mathrm{x}}{\mathrm{y}}} =?? \\ $$
Question Number 143962 Answers: 2 Comments: 0
$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{2}{xsin}^{\mathrm{2}} {t}}{{cos}^{\mathrm{2}} {t}+{x}^{\mathrm{2}} {sin}^{\mathrm{2}} {t}}{dt}=.....??? \\ $$
Question Number 143961 Answers: 1 Comments: 0
$$\mathrm{I}=\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{3}}} \frac{\mathrm{cos}^{\mathrm{6}} \mathrm{x}}{\mathrm{1}−\mathrm{3sin}^{\mathrm{2}} \mathrm{xcos}^{\mathrm{2}} \mathrm{x}}\mathrm{dx}=? \\ $$
Question Number 143960 Answers: 2 Comments: 0
$$\:\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}−\mathrm{cos}\:\mathrm{x}^{\mathrm{2}} }}{\mathrm{1}−\mathrm{cos}\:\mathrm{x}}\:=? \\ $$
Question Number 143959 Answers: 1 Comments: 0
$$\:\:\mathrm{If}\:\mathrm{g}\left(\mathrm{x}\right)=\left(\mathrm{4cos}\:^{\mathrm{4}} \mathrm{x}−\mathrm{2cos}\:\mathrm{2x}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{4x}−\mathrm{x}^{\mathrm{7}} \right)^{\frac{\mathrm{1}}{\mathrm{7}}} \\ $$$$\mathrm{then}\:\mathrm{tbe}\:\mathrm{value}\:\mathrm{of}\:\mathrm{g}\left(\mathrm{g}\left(\mathrm{100}\right)\right)\:\mathrm{is} \\ $$$$\mathrm{equal}\:\mathrm{to}\:... \\ $$
Question Number 143958 Answers: 1 Comments: 0
Question Number 143951 Answers: 0 Comments: 0
$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{2}{xsin}^{\mathrm{2}} {t}}{{cos}^{\mathrm{2}} {t}+{x}^{\mathrm{2}} {sin}^{\mathrm{2}} {t}}{dt}=.....???? \\ $$
Question Number 143952 Answers: 3 Comments: 0
Question Number 143920 Answers: 2 Comments: 0
Question Number 143913 Answers: 1 Comments: 0
$$\mathrm{If}\:\:\frac{\mathrm{cos}\:\alpha}{{cos}\:\beta}\:=\:\mathrm{m}\:\mathrm{and}\:\frac{\mathrm{cos}\:\alpha}{\mathrm{sin}\:\beta}\:=\:\mathrm{n}\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\left(\mathrm{m}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} \right)\mathrm{cos}^{\mathrm{2}} \beta\:=\:{n}^{\mathrm{2}} \\ $$
Question Number 143932 Answers: 4 Comments: 0
Question Number 143923 Answers: 0 Comments: 1
$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left[\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}\left(\frac{\mathrm{2}\pi}{\mathrm{3}}\right)\right)\right]? \\ $$
Question Number 143904 Answers: 1 Comments: 0
Question Number 143906 Answers: 1 Comments: 0
Question Number 143909 Answers: 2 Comments: 3
Question Number 143899 Answers: 3 Comments: 0
Question Number 143898 Answers: 0 Comments: 0
Question Number 143892 Answers: 0 Comments: 0
$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{cos}^{\mathrm{4}} \left(\mathrm{2x}\right)}{\left(\mathrm{x}^{\mathrm{4}} \:−\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$
Question Number 143890 Answers: 2 Comments: 0
$${if}\:{a}+{b}+{c}=\pi\:\:\: \\ $$$$\:{tanA}+{tanB}+{tanC}\:={tanA}.{tanB}.{tanC} \\ $$$$\mathrm{FAILED}\:\mathrm{TO}\:\mathrm{CALCULATE} \\ $$
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