Recent questions in Trigonometry

If $\sin\alpha+\sin\beta=\alpha$ and $\cos\alpha+\cos\beta=b$ then $\sin(\alpha+\beta)$ is equal to

asked Oct 14, 2013 by sreemathi.v

1 answer

If $\tan\alpha=\large\frac{1}{\sqrt{x(x^2+x+1)}}$ , $\tan\beta=\large\frac{\sqrt x}{\sqrt{x^2+x+1}}$ and $\tan\gamma=\sqrt{x^{-3}+x^{-2}+x^{-1}}$ then $\alpha+\beta$ is

asked Oct 14, 2013 by sreemathi.v

1 answer

If $\tan A-\tan B=x$ and $\cot B-\cot A=y$ then $\cot(A-B)$ is equal to

asked Oct 14, 2013 by sreemathi.v

1 answer

The value of $\sqrt{\large\frac{1+\cos\theta}{1-\cos\theta}}$ is equal to

asked Oct 14, 2013 by sreemathi.v

1 answer

The value of $\sqrt{\large\frac{1-\sin\theta}{1+\sin\theta}}$ is equal to

asked Oct 14, 2013 by sreemathi.v

1 answer

If $\alpha+\beta=\large\frac{\pi}{2}$ and $\beta+\gamma=\alpha$ then $\tan \alpha$ equals

asked Oct 14, 2013 by sreemathi.v

1 answer

The number of distinct real roots of $\begin{vmatrix}\sin x&\cos x&\cos x\\\cos x&\sin x&\cos x\\ \cos x&\cos x&\sin x\end{vmatrix}=0$ in the interval $-\large\frac{\pi}{4}$ $\leq x\leq \large\frac{\pi}{4}$ is

asked Oct 14, 2013 by sreemathi.v

1 answer

If $\large\frac{\sin^4x}{2}+\frac{\cos^4x}{3}=\frac{1}{5}$ then

asked Oct 14, 2013 by sreemathi.v

1 answer

The sides of a triangle inscribed in a given circle .Subtend angles of $\alpha,\beta$ and $\gamma$ at the centre.The minimum value of the arithemetic mean of $\cos(\alpha+\pi/2),\cos(\beta+\pi/2)$ and $\cos(\gamma+\pi/2)$ is equal to

asked Oct 14, 2013 by sreemathi.v

1 answer

The value of $\sin\large\frac{\pi}{14}$ $\sin\large\frac{3\pi}{4}$ $4\sin\large\frac{5\pi}{14}$ $\sin\large\frac{7\pi}{14}$ $\sin\large\frac{9\pi}{14}$ $\sin\large\frac{11\pi}{14}$ $\sin\large\frac{13\pi}{14}$ is equal to

asked Oct 11, 2013 by sreemathi.v

1 answer

Suppose $\sin^2x\sin 3x=\sum\limits_{m=0}^{n}C_m\cos mx$ is an identity in $x$ where $C_0,C_1.......C_n$ are constants and $C_n\neq 0$ then the value of n is

asked Oct 11, 2013 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 Oct 11, 2013 by sreemathi.v

1 answer

Evaluate $40^{\large\circ}30'$

asked Oct 11, 2013 by sreemathi.v

1 answer

If $x_1=2\tan^{-1}\big(\large\frac{1+x}{1-x}\big)$ $,x_2=\sin^{-1}\big[\large\frac{1-x^2}{1+x^2}\big]$ where $x\in(0,1)$ then $x_1+x_2$ is equal to

asked Oct 11, 2013 by sreemathi.v

1 answer

If $\cot(\cos^{-1}x)=\sec\big[\tan^{-1}\large\frac{a}{\sqrt{b^2-a^2}}\big]$ then $x$ is equal to

asked Oct 11, 2013 by sreemathi.v

1 answer

If $a=\sin^{-1}\big(\large\frac{-1}{\sqrt 2}\big)+$ $\cos^{-1}\big(\large\frac{-1}{2}\big),$ $b=\tan^{-1}\big(-\sqrt 3\big)-\cot^{-1}\big(-\large\frac{1}{\sqrt 3}\big)$ then

asked Oct 11, 2013 by sreemathi.v

1 answer

A solution of $\sin^{-1}(1)-\sin^{-1}\big(\large\frac{\sqrt 3}{x^2}\big)$ $-\large\frac{\pi}{6}$ $=0$ is

asked Oct 11, 2013 by sreemathi.v

1 answer

The value of $x$ satisfying $\sin^{-1}x+\sin^{-1}(1-x)=\cos^{-1}x$ are

asked Oct 11, 2013 by sreemathi.v

1 answer

The value of $\cos[2\tan^{-1}(-7)]$ is

asked Oct 11, 2013 by sreemathi.v

1 answer

If $\sin^{-1}x+\sin^{-1}y=\large\frac{\pi}{2}$ then $\cos^{-1}x+\cos^{-1}y$ is equal to

asked Oct 11, 2013 by sreemathi.v

1 answer

The principal value of $\sin^{-1}\tan\big(\large\frac{-5\pi}{4}\big)$ is

asked Oct 11, 2013 by sreemathi.v

1 answer

The value of $\cot (cosec^{-1}\large\frac{5}{3}$ $+\tan^{-1}\large\frac{2}{3})$ is

asked Oct 11, 2013 by sreemathi.v

1 answer