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Prove the following statement by the principle of mathematical induction : \[\] For any natural number $n$, $x^n-y^n$ is divisible by $x-y$, where $x$ and $y$ are any integers with $x \neq y$.

asked May 5, 2014 by thanvigandhi_1

0 answers

Prove the following statement by the principle of mathematical induction : \[\] For any natural number $n$, $7^{n}-2^n$ is divisible by 5.

asked May 5, 2014 by thanvigandhi_1

0 answers

Prove the following statement by the principle of mathematical induction : \[\] $3^{2n}-1$ is divisible by 8, for all natural numbers $n$.

asked May 5, 2014 by thanvigandhi_1

0 answers

Prove the following statement by the principle of mathematical induction : \[\] $n^{3}-7n+3$ is divisible by 3, for all natural numbers $n$.

asked May 5, 2014 by thanvigandhi_1

0 answers

Prove the following statement by the principle of mathematical induction : \[\] $2^{3n}-1$ is divisible by 7, for all natural numbers $n$.

asked May 5, 2014 by thanvigandhi_1

0 answers

Prove the following statement by the principle of mathematical induction : \[\] $4^n-1$ is divisible by 3, for each natural numbers $n$.

asked May 5, 2014 by thanvigandhi_1

0 answers

Give an example of a statement $P(n)$ which is true for all $n $. Justify your answer.

asked May 5, 2014 by thanvigandhi_1

0 answers

Give an example of a statement $P(n)$ which is true for all $ n \geq 4$ but $P(1), P(2)$ and $P(3)$ are not true. Justify your answer.

asked May 5, 2014 by thanvigandhi_1

0 answers

If $\sin x+\cos x=a$,then $|\sin x-\cos x|=$________

asked Apr 22, 2014 by sreemathi.v

1 answer

If $\sin x+\cos x=a$ then $\sin ^6x+\cos ^6x$=_______

asked Apr 22, 2014 by sreemathi.v

1 answer

If $\tan A=\large\frac{1-\cos B}{\sin B}$,then $\tan 2A$=_______

asked Apr 22, 2014 by sreemathi.v

1 answer

If $K=\sin\large\frac{5\pi}{8}$$\sin \large\frac{5\pi}{18}$$\sin \large\frac{7\pi}{18}$,then the numerical value of $K$ is _____

asked Apr 22, 2014 by sreemathi.v

1 answer

The value of $\large\frac{\sin 50^{\large\circ}}{\sin 130^{\large\circ}}$ is ________

asked Apr 22, 2014 by sreemathi.v

1 answer

If for real values of $x\cos\theta=x+\large\frac{1}{x}$,then

asked Apr 22, 2014 by sreemathi.v

2 answers

If $\tan \theta=\large\frac{a}{b}$,then $b\cos 2\theta+a\sin 2\theta$ is equal to

asked Apr 21, 2014 by sreemathi.v

1 answer

If $\tan\alpha=\large\frac{1}{7}$$,\tan \beta=\large\frac{1}{3}$,then $\cos 2\alpha$ is equal to

asked Apr 21, 2014 by sreemathi.v

1 answer

The value of $\cos^248^{\large\circ}-\sin^212^{\large\circ}$ is

asked Apr 21, 2014 by sreemathi.v

1 answer

If $A$ lies in the second quadrant and $3\tan A+4=0$,then the value of $2\cot A-5\cos A+\sin A$ is equal to

asked Apr 21, 2014 by sreemathi.v

1 answer

The value of $\sin\large\frac{\pi}{18}$$+\sin \large\frac{\pi}{9}$$+\sin \large\frac{2\pi}{9}$$+\sin \large\frac{5\pi}{18}$ is given by

asked Apr 21, 2014 by sreemathi.v

1 answer

Number of solutions of the equation $\tan x+\sec x=2\cos x$ lying in the interval $[0,2\pi]$ is

asked Apr 21, 2014 by sreemathi.v

1 answer

If $\sin \theta=-\large\frac{4}{5}$ and $\theta$ lies in third quadrant then the value of $\cos\large\frac{\theta}{2}$ is

asked Apr 21, 2014 by sreemathi.v

1 answer

If $\alpha+\beta=\large\frac{\pi}{4}$,then the value of $(1+\tan \alpha)-(1+\tan \beta)$ is

asked Apr 21, 2014 by sreemathi.v

1 answer

If $\sin \theta+\cos \theta=1$,then the value of $\sin 2\theta$ is equal to

asked Apr 21, 2014 by sreemathi.v

1 answer

The value of $\sin 50^{\large\circ}-\sin 70^{\large\circ}+\sin 10^{\large\circ}$ is

asked Apr 21, 2014 by sreemathi.v

1 answer

The value of $\sin\large\frac{\pi}{10}$$\sin\large\frac{13\pi}{10}$ is

asked Apr 21, 2014 by sreemathi.v

1 answer

$\tan A=\large\frac{1}{2}$$,\tan B=\large\frac{1}{3}$,then $\tan (2A+B)$ is equal to

asked Apr 21, 2014 by sreemathi.v

1 answer

The value of $\cos 12^{\large\circ}+\cos 84^{\large\circ}+\cos 156^{\large\circ}+\cos 132^{\large\circ}$ is

asked Apr 21, 2014 by sreemathi.v

1 answer

$\cos 2\theta\cos 2\phi+\sin^2(\theta-\phi)-\sin^2(\theta+\phi)$ is equal to

asked Apr 21, 2014 by sreemathi.v

1 answer

The value of $\cot(\large\frac{\pi}{4}+$$\theta).\cot(\large\frac{\pi}{4}$$-\theta)$ is

asked Apr 21, 2014 by sreemathi.v

1 answer

The value of $\sin (45^{\large\circ}+\theta)-\cos(45^{\large\circ}-\theta)$ is

asked Apr 21, 2014 by sreemathi.v

1 answer

The value of $\tan 3A-\tan 2A-\tan A$ is equal to

asked Apr 21, 2014 by sreemathi.v

1 answer

If $\tan\alpha=\large\frac{m}{m+1}$$,\tan \beta=\large\frac{1}{2m+1}$,then $\alpha+\beta$ is equal to

asked Apr 21, 2014 by sreemathi.v

1 answer

Which of the following is correct

asked Apr 21, 2014 by sreemathi.v

0 answers

The value of $\tan 75^{\large\circ}-\cot 75^{\large\circ}$ is equal to

asked Apr 21, 2014 by sreemathi.v

1 answer

If $\tan\theta=3$ and $\theta$ lies in third quadrant then the value of $\sin \theta$ is

asked Apr 21, 2014 by sreemathi.v

1 answer

The value of $\cos 1^{\large\circ}\cos 2^{\large\circ}\cos 3^{\large\circ}.......\cos 179^{\large\circ}$ is

asked Apr 21, 2014 by sreemathi.v

1 answer

The value of $\large\frac{1-\tan^215}{1+\tan^215}$ is

asked Apr 21, 2014 by sreemathi.v

1 answer

The value of $\tan 1^{\large\circ}\tan 2^{\large\circ}\tan 3^{\large\circ}$........$\tan 89^{\large\circ}$ is

asked Apr 21, 2014 by sreemathi.v

1 answer

If $\tan \theta=\large\frac{1}{2}$ and $\tan\phi=\large\frac{1}{3}$,then the value of $\theta+\phi$ is

asked Apr 21, 2014 by sreemathi.v

1 answer

If $f(x)=\cos^2x+\sec^2x$,then

asked Apr 21, 2014 by sreemathi.v

1 answer

If $\sin \theta+cosec\theta=2$,then $\sin^2\theta+cosec^2\theta$ is equal to

asked Apr 21, 2014 by sreemathi.v

1 answer

Find the general solution of the equation $\sin x-3\sin 2x+\sin 3x=\cos x-3\cos 2x+\cos 3x$

asked Apr 21, 2014 by sreemathi.v

1 answer

Find the general solution of the equation $5\cos^2\theta+7\sin^2\theta-6=0$

asked Apr 21, 2014 by sreemathi.v

1 answer

Find the value of the expression :$\cos^4\large\frac{\pi}{8}$$+\cos^4\large\frac{3\pi}{8}$$+\cos^4\large\frac{5\pi}{8}$$+\cos^4\large\frac{7\pi}{8}$

asked Apr 21, 2014 by sreemathi.v

1 answer

If $\theta$ lies in the first quadrant and $\cos\theta=\large\frac{8}{17}$,then the value of $\cos(30^{\large\circ}+\theta)+\cos(45^{\large\circ}-\theta)+\cos(120^{\large\circ}-\theta)$ ?

asked Apr 20, 2014 by sreemathi.v

1 answer

If $x=\sec\phi-\tan\phi$ and $y=cosec\phi+\cot \phi$ then show that $xy+x-y+1=0$

asked Apr 20, 2014 by sreemathi.v

1 answer

If $a\cos 2\theta+b\sin 2\theta=c$ has $\alpha$ and $\beta$ as its roots,then prove that $\tan\alpha+\tan \beta=\large\frac{2b}{a+c}$

asked Apr 20, 2014 by sreemathi.v

1 answer

Find the value of the expression :$3[\sin^4(\large\frac{3\pi}{2}-\normalsize\alpha)+\sin^4(3\pi+\alpha)]-2[\sin^6(\large\frac{\pi}{2}+\normalsize \alpha)+\sin^6(5\pi-\alpha)]$

asked Apr 20, 2014 by sreemathi.v

1 answer

If $\cos(\theta+\phi)=m\cos(\theta-\phi)$ then prove that $\tan\theta=\large\frac{1-m}{1+m}$$\cot\phi$

asked Apr 20, 2014 by sreemathi.v

1 answer

If $\sin(\theta+\alpha)=a$ and $\sin(\theta+\beta)=b$,then prove that $\cos 2(\alpha-\beta)-4ab\cos(\alpha-\beta)=1-2a^2-2b^2$

asked Apr 20, 2014 by sreemathi.v

1 answer

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