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Question Number 143960 Answers: 2 Comments: 0

The value of lim_(x→0) ((√(1−cos x^2 ))/(1−cos x)) =?

$$\:\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}−\mathrm{cos}\:\mathrm{x}^{\mathrm{2}} }}{\mathrm{1}−\mathrm{cos}\:\mathrm{x}}\:=? \\ $$

Question Number 143959 Answers: 1 Comments: 0

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 ...

$$\:\:\mathrm{If}\:\mathrm{g}\left(\mathrm{x}\right)=\left(\mathrm{4cos}\:^{\mathrm{4}} \mathrm{x}−\mathrm{2cos}\:\mathrm{2x}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{4x}−\mathrm{x}^{\mathrm{7}} \right)^{\frac{\mathrm{1}}{\mathrm{7}}} \\ $$$$\mathrm{then}\:\mathrm{tbe}\:\mathrm{value}\:\mathrm{of}\:\mathrm{g}\left(\mathrm{g}\left(\mathrm{100}\right)\right)\:\mathrm{is} \\ $$$$\mathrm{equal}\:\mathrm{to}\:... \\ $$

Question Number 143958 Answers: 1 Comments: 0

Question Number 143951 Answers: 0 Comments: 0

∫_0 ^(π/2) ((2xsin^2 t)/(cos^2 t+x^2 sin^2 t))dt=.....????

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{2}{xsin}^{\mathrm{2}} {t}}{{cos}^{\mathrm{2}} {t}+{x}^{\mathrm{2}} {sin}^{\mathrm{2}} {t}}{dt}=.....???? \\ $$

Question Number 143952 Answers: 3 Comments: 0

Question Number 143920 Answers: 2 Comments: 0

Question Number 143913 Answers: 1 Comments: 0

If ((cos α)/(cos β)) = m and ((cos α)/(sin β)) = n then prove that (m^2 +n^2 )cos^2 β = n^2

$$\mathrm{If}\:\:\frac{\mathrm{cos}\:\alpha}{{cos}\:\beta}\:=\:\mathrm{m}\:\mathrm{and}\:\frac{\mathrm{cos}\:\alpha}{\mathrm{sin}\:\beta}\:=\:\mathrm{n}\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\left(\mathrm{m}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} \right)\mathrm{cos}^{\mathrm{2}} \beta\:=\:{n}^{\mathrm{2}} \\ $$

Question Number 143932 Answers: 4 Comments: 0

Question Number 143923 Answers: 0 Comments: 1

What is the value of [sin^(−1) (sin(((2π)/3)))]?

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left[\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}\left(\frac{\mathrm{2}\pi}{\mathrm{3}}\right)\right)\right]? \\ $$

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

calculate ∫_0 ^∞ ((cos^4 (2x))/((x^4 −x^2 +1)^2 ))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{cos}^{\mathrm{4}} \left(\mathrm{2x}\right)}{\left(\mathrm{x}^{\mathrm{4}} \:−\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 143890 Answers: 2 Comments: 0

if a+b+c=π tanA+tanB+tanC =tanA.tanB.tanC FAILED TO CALCULATE

$${if}\:{a}+{b}+{c}=\pi\:\:\: \\ $$$$\:{tanA}+{tanB}+{tanC}\:={tanA}.{tanB}.{tanC} \\ $$$$\mathrm{FAILED}\:\mathrm{TO}\:\mathrm{CALCULATE} \\ $$

Question Number 143897 Answers: 1 Comments: 0

Question Number 143878 Answers: 3 Comments: 0

y′′′=2xy′′

$$\mathrm{y}'''=\mathrm{2xy}'' \\ $$

Question Number 143875 Answers: 0 Comments: 1

Question Number 143874 Answers: 0 Comments: 0

y′′−x×y′′′+y′′′^3 =0

$$\mathrm{y}''−\mathrm{x}×\mathrm{y}'''+\mathrm{y}'''^{\mathrm{3}} =\mathrm{0} \\ $$

Question Number 143863 Answers: 0 Comments: 1

Question Number 143860 Answers: 1 Comments: 0

calculate ∫_0 ^∞ x e^(−x^2 ) log(1+e^x )dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\mathrm{x}\:\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } \mathrm{log}\left(\mathrm{1}+\mathrm{e}^{\mathrm{x}} \right)\mathrm{dx} \\ $$

Question Number 143858 Answers: 1 Comments: 0

if A≥0, B≥0, A+B=(Π/3) then find minimum and maximum of tan A.tan B

$$\mathrm{if}\:\mathrm{A}\geqslant\mathrm{0},\:\mathrm{B}\geqslant\mathrm{0},\:\mathrm{A}+\mathrm{B}=\frac{\Pi}{\mathrm{3}}\:\mathrm{then} \\ $$$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{and}\:\mathrm{maximum}\: \\ $$$$\mathrm{of}\:\mathrm{tan}\:\mathrm{A}.\mathrm{tan}\:\mathrm{B}\: \\ $$

Question Number 143857 Answers: 0 Comments: 0

if cos^4 θsec^2 α, (1/2), sin^4 θcosec^2 α are in A.P. then cos^8 θsec^6 α, (1/2), sin^8 θcosec^6 α are in which progression?

$$\mathrm{if}\:\mathrm{cos}^{\mathrm{4}} \theta\mathrm{sec}\:^{\mathrm{2}} \alpha,\:\frac{\mathrm{1}}{\mathrm{2}},\:\mathrm{sin}^{\mathrm{4}} \theta\mathrm{cosec}^{\mathrm{2}} \alpha\: \\ $$$$\mathrm{are}\:\mathrm{in}\:\mathrm{A}.\mathrm{P}.\:\mathrm{then} \\ $$$$\:\mathrm{cos}^{\mathrm{8}} \theta\mathrm{sec}^{\mathrm{6}} \alpha,\:\frac{\mathrm{1}}{\mathrm{2}},\:\mathrm{sin}^{\mathrm{8}} \theta\mathrm{cosec}^{\mathrm{6}} \alpha \\ $$$$\mathrm{are}\:\mathrm{in}\:\mathrm{which}\:\mathrm{progression}? \\ $$

Question Number 143868 Answers: 2 Comments: 1

Question Number 143850 Answers: 0 Comments: 0

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