Search results

Thanks friends got it although i have solved using Very Lengthy Method. but Here Moderator solution is very short. Thanks

Can we Write the given Trigonometric exprission into Closed form \displaystyle \cos \left(\frac{x}{2}\right)+\cos \left(\frac{x}{4}\right)+\cos \left(\frac{x}{8}\right)+...........+\cos \left(\frac{x}{128}\right)

Let a_{1},a_{2},a_{3}......,a_{10} be a permutation of the set \left\{1,2,3......,10 \right\} such that the sequence a_{i} decreases first and then increases like 8,6,4,1,2,3,5,7,9,10. If N is the number of such permutations,then the sum of digits of N is

\int \tan (x).\sec (2x)dx

\hspace{-16}$If%20Your%20Question%20is%20Something%20like%20that%20$\bf{\lim_{n\rightarrow%20\infty}\sum_{k=1}^{n}\frac{k}{5^k}}$\\\\\\%20Answer.....\\\\\\%20Let%20$\bf{\mathbb{S}=\lim_{n\rightarrow%20\infty}\sum_{k=1}^{n}\frac{k}{5^k}}$\\\\\\\%20Replace%20$\bf{k\rightarrow%20(k+1)}$\\\\\\%20$\bf...

Thanks friends I have solved in same way.....

\hspace{-16}$%20Let%20$\bf{\omega}$%20be%20a%20cube%20root%20of%20unity%20which%20is%20not%20equal%20to%20$1$.\\\\%20Then%20the%20number%20of%20distinct%20elements%20in%20the%20set%20$\bf{{(1+\omega+\omega^2+\omega^3+...+\omega^n)^m}$\\\\%20Where%20$\bf{m,n=\left\{1,2,3,...\right\}}}$.

\displaystyle \int \sqrt{x+\sqrt{x^2+2}}\; dx

I did not Understand that line If the equality signs in the second condition are changed to addition signs, then the question is more interesting. The answer is: -13 =< abc =< 243 using the cubic discriminant. Could you like to explain it to me. Thanks

Thanks Moderator I did not Understand How can I get value of \cot(1^0).\cot(2^0)......\cot(44^0) Using above formula. Thanks

\hspace{-16}\bf{\int%20\sec%20{x}dx=\int\frac{\sec%20x.(\sec%20x+\tan%20x)}{\sec%20x+\tan%20x}dx}$\\\\\\%20Now%20Put%20$\bf{\sec%20x+\tan%20x=t\Leftrightarrow%20\sec%20x(\tan%20x+\sec%20x)dx%20=%20dt}$\\\\\\%20So%20$\bf{\int%20\frac{1}{t}dt=\ln%20\mid%20t%20\mid+\mathbb{C}=\ln%20\mid%20\sec%20x+\...

Sorry friends actually it is ab = bc = ca = 25

Thanks Moderator But when i have searched Then I have found following values of product of sin and cos , which is Given below...

\hspace{-16}\mathbb{I}$f%20$\bf{a\;,b\;,c}$%20are%20$\bf{3}$%20Real%20no.%20Such%20that%20$\bf{a+b+c=15}$%20and%20$\bf{ab=bc=ca=27}$\\\\%20Then%20Range%20of%20The%20expression%20$\bf{abc}$%20is

\hspace{-16}$Can%20we%20calculate%20the%20product%20of\\\\\\%20$\bf{\cot(1^0).\cot(2^0).\cot(3^0)..........\cot(44^0)=}$\\\\\\%20Where%20all%20angle%20are%20in%20Degree. like by using Trigonometry OR Using Complex no. can anyone help me to solve the Given Question Thanks

(4)...

Re: 2012 HSC MX2 Marathon \hspace{-16}\bf{\int\frac{1}{1+x^4}dx}

Re: 2012 HSC MX2 Marathon another solution Using Trigonometry...

Re: 2012 HSC MX2 Marathon...

I have tried like that...