Recent questions tagged bookproblem

Prove the following by using the principle of mathematical induction for all $ n \in N $ \[\] $1.3+2.3^2+3.3^3+...+n.3^n=\large\frac{(2n-1)3^{n+1}+3}{4}$

asked Apr 29, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all $ n \in N $ \[\] $1.2.3 + 2.3.4+...+n(n+1)(n+2)= \large\frac{n(n+1)(n+2)(n+3)}{4}$

asked Apr 29, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $1+ \large\frac{1}{(1+2)}$$+ \large\frac{1}{(1+2+3)}$$+...+ \large\frac{1}{(1+2+3...n)}$$= \large\frac{2n}{(n+1)}$

asked Apr 29, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all $n \in N $: \[\] $1^3+2^3+3^3+...+n^3= \bigg( \large\frac{n(n+1)}{2} \bigg)^2$

asked Apr 29, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all $n \in N$ : \[\] $1+3+3^2+...+3^{n-1}= \large\frac{(3^n-1)}{2}$

asked Apr 29, 2014 by thanvigandhi_1

1 answer

Find $\sin \large\frac{x}{2},$$\cos \large\frac{x}{2}$ and $\tan \large\frac{x}{2}$ when $\cos x=-\large\frac{1}{3}$.$x$ in quadrant III

asked Apr 18, 2014 by sreemathi.v

1 answer

Find $\sin \large\frac{x}{2},$$\cos \large\frac{x}{2}$ and $\tan \large\frac{x}{2}$ when $\tan x=-\large\frac{4}{3}$,$x$ in quadrant II

asked Apr 18, 2014 by sreemathi.v

1 answer

Evaluate $\sin 3x+\sin 2x-\sin x=4\sin x\cos\large\frac{x}{2}$$\cos\large\frac{3x}{2}$

asked Apr 18, 2014 by sreemathi.v

1 answer

Prove that $\large\frac{(\sin 7x+\sin 5x)+(\sin 9x+\sin 3x)}{(\cos 7x+\cos 5x)+(\cos 9x+\cos 3x)}$$=\tan 6x$

asked Apr 18, 2014 by sreemathi.v

1 answer

Evaluate $\sin x+\sin 3x+\sin 5x+\sin 7x$

asked Apr 18, 2014 by sreemathi.v

1 answer

Prove that $(\cos x-\cos y)^2+(\sin x-\sin y)^2=4\sin^2\large\frac{x-y}{2}$

asked Apr 18, 2014 by sreemathi.v

1 answer

Evaluate: $(\cos x+\cos y)^2+(\sin x-\sin y)^2$

asked Apr 18, 2014 by sreemathi.v

1 answer

Prove that $(\sin 3x+\sin x)\sin x+(\cos 3x-\cos x)\cos x=0$

asked Apr 18, 2014 by sreemathi.v

1 answer

Evaluate:$2\cos\large\frac{\pi}{13}$$\cos \large\frac{9\pi}{13}+$$\cos \large\frac{3\pi}{13}$$+\cos \large\frac{5\pi}{13}$

asked Apr 18, 2014 by sreemathi.v

1 answer

Find the general solution for the equation $\sin x+\sin 3x+\sin 5x=0$

asked Apr 18, 2014 by sreemathi.v

1 answer

Find the general solution for each of the following equation $\sec^22x=1-\tan 2x$

asked Apr 18, 2014 by sreemathi.v

1 answer

Find the general solution for the equation $\sin 2x+\cos x=0$

asked Apr 18, 2014 by sreemathi.v

1 answer

Find the general solution for the equation $\cos 3x+\cos x-\cos 2x=0$

asked Apr 18, 2014 by sreemathi.v

1 answer

Find the general solution for each of the following equation $\cos 4x=\cos 2x$

asked Apr 18, 2014 by sreemathi.v

1 answer

Verify that $(-1,2,1),\:(1,-2,5),\:(4,-7,8)\:and\:(2,-3,4)$ are vertices of a parallelogram.

asked Apr 17, 2014 by rvidyagovindarajan_1

1 answer

Verify that $(0,7,10),\:(-1,6,6)\:and\:(-4,9,6)$ are vertices of a right angled triangle.

asked Apr 17, 2014 by rvidyagovindarajan_1

1 answer