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Recent questions tagged ch3

Prove that $\cos (45^{\large\circ}-A).\cos(45^{\large\circ}-B)-\sin(45^{\large\circ}-A)\sin(45^{\large\circ}-B)=\sin(A+B)$

asked May 21, 2014 by sreemathi.v

1 answer

If $A$ and $B$ are positive acute angle and $\cos A=\large\frac{1}{7},$$\cos B=\large\frac{13}{14}$,then show that $A-B=60^{\large\circ}$

asked May 21, 2014 by sreemathi.v

1 answer

Evaluate :$\sin(n\pi+(-1)^n\large\frac{\pi}{4})$ where $n$ is an integer,

asked May 21, 2014 by sreemathi.v

1 answer

Evaluate $\tan 75^{\large\circ}+\cot 75^{\large\circ}$

asked May 21, 2014 by sreemathi.v

1 answer

Find the value of $\tan 105^{\large\circ}$

asked May 21, 2014 by sreemathi.v

1 answer

Evaluate $\sin 105^{\large\circ}+\cos 105^{\large\circ}$

asked May 21, 2014 by sreemathi.v

1 answer

Find the value $\tan 330^{\large\circ}$

asked May 21, 2014 by sreemathi.v

1 answer

Find the value of $\mathrm{cosec}(-1410^{\large\circ})$

asked May 21, 2014 by sreemathi.v

1 answer

Find the degree measure of $(-2)^c$

asked May 21, 2014 by sreemathi.v

1 answer

If the arcs of the same length in two circles subtend angles of $60^{\large\circ}$ and $75^{\large\circ}$ at their respective centres,find the ratio of their radii

asked May 21, 2014 by sreemathi.v

1 answer

In right-angled triangle, the difference between the two acute angles is $(\large\frac{\pi}{15})^c$.Find the angles in degrees

asked May 20, 2014 by sreemathi.v

1 answer

Evaluate : $\cot ^4\theta+\cot ^2\theta$

asked May 20, 2014 by sreemathi.v

1 answer

Find the radian measure of $-37^{\large\circ}30'$

asked May 20, 2014 by sreemathi.v

1 answer

Find the degree measure of $(\large\frac{7\pi}{12})^c$

asked May 20, 2014 by sreemathi.v

1 answer

The angles of a triangle are in the ratio 3 : 4 : 5.Find the smallest angle in degrees and the greatest angle in radians

asked May 20, 2014 by sreemathi.v

1 answer

In a circle of diameter 50cm,the length of a chord is 25cm.Find the length of the minor arc of the chord

asked May 20, 2014 by sreemathi.v

1 answer

Find the radius of the circle in which a central angle of $45^{\large\circ}$ intercepts an arc 132cm

asked May 20, 2014 by sreemathi.v

1 answer

The wheel of a railway carriage is 40cm in diameter and makes 6 revolutions in a second. How fast is the train going?

asked May 20, 2014 by sreemathi.v

2 answers

In the following match each item given under the column $C_1$ to its correct answer given under the column $C_2$

asked May 20, 2014 by sreemathi.v

1 answer

True-or-False :If $\tan(\pi \cos \theta)=\cot (\pi \sin \theta)$,then $\cos(\theta-\large\frac{\pi}{4})$$=\pm \large\frac{1}{2\sqrt 2}$

asked May 20, 2014 by sreemathi.v

1 answer

True-or-False :If $\tan \theta+\tan 2\theta+\sqrt 3\tan \theta\tan 2\theta=\sqrt 3$ then $\theta=\large\frac{n\pi}{3}+\frac{\pi}{9}$

asked May 20, 2014 by sreemathi.v

1 answer

True-or-False :If $cosec x=1+\cot x$ then $x=2n\pi,2n\pi+\large\frac{\pi}{2}$

asked May 20, 2014 by sreemathi.v

1 answer

True-or-False :One value of $\theta$ which satisfies the equation $\sin ^4\theta-2\sin ^2\theta-1$ lies between 0 and $2\pi$

asked May 20, 2014 by sreemathi.v

1 answer

True-or-False :$\cos \large\frac{2\pi}{15}$$\cos \large\frac{4\pi}{15}$$\cos \large\frac{8\pi}{15}$$\cos \large\frac{16\pi}{15}=\frac{1}{16}$

asked May 20, 2014 by sreemathi.v

0 answers

True-or-False :$\sin 10^{\large\circ}$ is greater than $\cos 10^{\large\circ}$

asked May 20, 2014 by sreemathi.v

1 answer

True-or-False :The equality $\sin A+\sin 2A+\sin 3A=3$ holds for some real value of A

asked May 20, 2014 by sreemathi.v

1 answer

True-or-False :If $\tan A=\large\frac{1-\cos B}{\sin B}$ then $\tan 2A=\tan B$

asked May 20, 2014 by sreemathi.v

1 answer

The maximum distance of a point on the graph of the function $y=\sqrt 3\sin x+\cos x$ from $x$-axis is ________

asked May 20, 2014 by sreemathi.v

1 answer

Given $x > 0$,the value of $f(x)=-3\cos \sqrt{3+x+x^2}$ lie in the interval _________

asked May 20, 2014 by sreemathi.v

1 answer

$3(\sin x-\cos x)^4+6(\sin x+\cos x)^2+4(\sin ^6x+\cos ^6x)$=_______

asked May 20, 2014 by sreemathi.v

1 answer

In a triangle ABC with $\angle C=90^{\large\circ}$ the equation whose roots are $\tan A$ and $\tan B$ is ___________

asked May 20, 2014 by sreemathi.v

1 answer

Which of the following is correct?

asked May 20, 2014 by sreemathi.v

1 answer

Which of the following is not correct ?

asked May 20, 2014 by sreemathi.v

1 answer

Find the general solution of the equation $(\sqrt 3+1)\cos \theta+(\sqrt 3-1)\sin \theta=2$

asked May 20, 2014 by sreemathi.v

1 answer

Prove that $\cos \theta \cos\large\frac{\theta}{2}-$$\cos 3\theta\cos \large\frac{9\theta}{2}=$$\sin 7\theta\sin 8\theta$

asked May 20, 2014 by sreemathi.v

1 answer

If $A,B$ are two square matrices such that $AB=A$ and $BA=B$ then $A$ and $B$ are

asked Apr 25, 2014 by sreemathi.v

1 answer

If $A$ is orthogonal matrix then

asked Apr 25, 2014 by sreemathi.v

1 answer

The number of right inverse for the matrix $\begin{bmatrix}1&-1&2\\2&-1&1\end{bmatrix}$

asked Apr 25, 2014 by sreemathi.v

1 answer

If $A$ is an invertible matrix and B is a matrix then

asked Apr 24, 2014 by sreemathi.v

1 answer

$\begin{vmatrix}\log_3512&\log_43\\\log_38&\log_49\end{vmatrix}\times \begin{vmatrix}\log_23&\log_83\\\log_34&\log_34\end{vmatrix}=$

asked Apr 24, 2014 by sreemathi.v

1 answer

Let $C=\begin{bmatrix}C_{11}&C_{12}\\C_{21}&C_{22}\end{bmatrix}$ be a $2\times 2$ matrix and there exist $2\times 2$ matrices $A$ and $B$ such that $C=AB-BA$ then

asked Apr 24, 2014 by sreemathi.v

1 answer

If $a,b,c$ are all different and $\begin{vmatrix}a&a^3&a^4-1\\b&b^3&b^4-1\\c&c^3&c^4-1\end{vmatrix}=0$ then the value of $abc(ab+bc+ca)$ is

asked Apr 23, 2014 by sreemathi.v

1 answer

The value of $\theta$ in the first quadrant satisfying the equation $\begin{vmatrix}1+\cos^2\theta&\sin^2\theta&4\sin 4\theta\\\cos^2\theta&1+\sin^2\theta&4\sin4\theta\\\cos^2\theta&\sin^2\theta&1+4\sin 4\theta\end{vmatrix}=0$ is

asked Apr 23, 2014 by sreemathi.v

1 answer

If $a=1+2+4+.........$upto n terms,$b=1+3+9+.....$upto n terms,$c=1+5+25+.....$upto n terms then $\begin{vmatrix}a&2b&4c\\2&2&2\\2^n&3^n&5^n\end{vmatrix}=$

asked Apr 23, 2014 by sreemathi.v

1 answer

The value of $\begin{vmatrix}a&a+b&a+2b\\a+2b&a&a+b\\a+b&a+2b&a\end{vmatrix}$ is equal to

asked Apr 23, 2014 by sreemathi.v

1 answer

If $f(x)=\begin{vmatrix}\sin x&\cos x&\tan x\\x^3&x^2&x\\2x&1&1\end{vmatrix}$ then $\lim\limits_{x\to 0}\large\frac{f(x)}{x^2}$ is

asked Apr 23, 2014 by sreemathi.v

1 answer

If $p\neq a,q\neq b,r\neq c$ and $\begin{vmatrix}p&b&c\\p+a&q+b&2c\\a&b&r\end{vmatrix}=0$ then $\large\frac{p}{p-a}+\frac{q}{q-b}+\frac{r}{r-c}$=

asked Apr 23, 2014 by sreemathi.v

1 answer

If $A=\begin{bmatrix}0&2\\3&-4\end{bmatrix}$ and $kA=\begin{bmatrix}0&3a\\2b&24\end{bmatrix}$ then the values of $k,a,b$ are respectively

asked Apr 23, 2014 by sreemathi.v

1 answer

If $A=\begin{bmatrix}2&0&0\\0&2&0\\0&0&2\end{bmatrix}$ then $A^5=$

asked Apr 23, 2014 by sreemathi.v

1 answer

If $\begin{vmatrix}x+\alpha&\beta&\gamma\\\alpha&x+\beta&\gamma\\\alpha&\beta&x+\gamma\end{vmatrix}=0$ then $4x$ is equal to

asked Apr 23, 2014 by sreemathi.v

1 answer

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