Recent questions in Trigonometry

The smallest positive value of $x$ (in degrees) for which $\tan ( x+100 ^{\circ}$ $)=\tan (x+50^{\circ}) \times \tan x \times \tan (x-50^{\circ})$

asked Oct 18, 2013 by sreemathi.v

1 answer

If $\tan\alpha=\large\frac{p}{q}$ where $\alpha=6\beta$ . $\alpha$ being acute angle,then $\large\frac{1}{2}$ $[p\; \mathrm{ cosec} 2\beta-q\sec 2\beta]$ is equal to

asked Oct 18, 2013 by sreemathi.v

1 answer

The value of $\large\frac{\sec 8\theta-1}{\sec 4\theta-1}$ is equal to

asked Oct 18, 2013 by sreemathi.v

1 answer

If $\alpha,\beta,\gamma\in (0,\large\frac{\pi}{2})$ then $\sin\alpha+\sin\beta+\sin\gamma$ is

asked Oct 18, 2013 by sreemathi.v

1 answer

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

asked Oct 18, 2013 by sreemathi.v

1 answer

If $x=\sin^{14}\theta+\cos ^{20}\theta$ ,then for all $\theta\in R$

asked Oct 18, 2013 by sreemathi.v

1 answer

In a $\Delta PQR$ if $3\sin P+4\cos Q=6.4\sin Q+3\cos P=1$ then the angle $R$ is equal to

asked Oct 17, 2013 by sreemathi.v

1 answer

If $u=\sqrt{a^2\cos^2\theta+b^2\sin^2\theta}+\sqrt{a^2\sin^2\theta+b^2\cos^2\theta}$ then the difference between the maximum and minimum values of $u^2$ is given by

asked Oct 17, 2013 by sreemathi.v

1 answer

Let $A$ and $B$ denote the statements $A=\cos \alpha+\cos \beta+\cos\gamma=0,B=\sin\alpha+\sin\beta+\sin\gamma=0$ .If $\cos(\beta-\gamma)+\cos(\gamma-\alpha)+\cos(\alpha-\beta)=-\large\frac{3}{2}$ then

asked Oct 17, 2013 by sreemathi.v

1 answer

The number of solutions of the pair of equations $2\sin^2\theta-\cos 2\theta=0,2\cos^2\theta-3\sin\theta=0$ in the interval $[0,2\pi]$ is

asked Oct 17, 2013 by sreemathi.v

1 answer

Given both $\theta$ and $\phi$ are acute angles and $\sin\theta=\large\frac{1}{2},$ $\cos\phi=\large\frac{1}{3}$ then the value of $\theta+\phi$ belongs to

asked Oct 17, 2013 by sreemathi.v

1 answer

The solution set of the system of equational $x+y=\large\frac{2\pi}{3}$ $,\cos x+\cos y=\large\frac{3}{2}$ where $x$ and $y$ are real is

asked Oct 17, 2013 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 Oct 17, 2013 by sreemathi.v

1 answer

$\tan 5^{\large\circ}$ is a

asked Oct 17, 2013 by sreemathi.v

1 answer

If $\pi < \theta < \large\frac{3\pi}{2}$ the expression $\sqrt{4\sin^4\theta+\sin^22\theta}+4\cos^2\big(\large\frac{\pi}{4}-\frac{\theta}{2}\big)$ is equal to

asked Oct 17, 2013 by sreemathi.v

1 answer

If $p=\cos 55^{\large\circ},q=\cos 65^{\large\circ}$ and $r=\cos 175^{\large\circ}$ then the value of $\large\frac{1}{p}+\frac{1}{q}+\frac{r}{pq}$ is

asked Oct 17, 2013 by sreemathi.v

1 answer

Evaluate : $\sin^{-1}\large\frac{4}{5}$ $+\sin^{-1}\large\frac{5}{13}$ $+\sin^{-1}\large\frac{16}{65}$

asked Oct 17, 2013 by sreemathi.v

1 answer

Find the value of $\tan\big[\large\frac{1}{2}$ $\big(\sin^{-1}\large\frac{2x}{1+x^2}+$ $\cos^{-1}\large\frac{1-y^2}{1+y^2}\big)\big],$ $\mid x\mid < 1,y > 0$ and $xy <1$

asked Oct 17, 2013 by sreemathi.v

1 answer

Evaluate : $\tan\big[\large\frac{1}{2}$ $\cos^{-1}\large\frac{\sqrt 5}{3}\big]$

asked Oct 17, 2013 by sreemathi.v

1 answer

Simplify : $\large\frac{\sin 7x-\sin 3x-\sin 5x+\sin x}{\cos 7x+\cos 3x-\cos 5x-\cos x}$

asked Oct 16, 2013 by sreemathi.v

1 answer

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

asked Oct 16, 2013 by sreemathi.v

1 answer

If $\tan\theta+\tan\big(\theta+\large\frac{\pi}{3}\big)$ $+\tan\big(\theta+\large\frac{2\pi}{3}\big)$ $=3$ then which of the following is equal to 1.

asked Oct 16, 2013 by sreemathi.v

1 answer

Simplify : $\large\frac{\sin\big(\Large\frac{3\pi}{2}-\theta\big)\cos\big(\Large\frac{\pi}{2}+\theta\big)}{\tan\big(\Large\frac{\pi}{2}+\theta\big)}-\frac{\sin\big(\Large\frac{3\pi}{2}-\theta\big)}{\sec\big(\pi+\theta\big)}$

asked Oct 16, 2013 by sreemathi.v

1 answer

$\cot^{-1}\big(\sqrt{\cos\alpha}-\tan^{-1}(\sqrt{\cos\alpha}\big)=x$ then $\sin x=?$

asked Oct 16, 2013 by sreemathi.v

1 answer

Evaluate : $\large\frac{1+\sin\theta-\cos\theta}{1+\sin\theta+\cos\theta}$

asked Oct 16, 2013 by sreemathi.v

1 answer

Find $\cos\tan^{-1}\sin\cot^{-1}x$

asked Oct 16, 2013 by sreemathi.v

1 answer

If $\tan\theta=\large\frac{b}{a}$ then find the value of $a^2\cos 2\theta+b\sin 2\theta$

asked Oct 16, 2013 by sreemathi.v

1 answer

The value of $\cot\sum\limits_{n=1}^{23}\cot^{-1}\big(1+\sum\limits_{k=1}^n 2k\big)$ is

asked Oct 16, 2013 by sreemathi.v

1 answer

The value of $\sin 36^{\large\circ}\sin 72^{\large\circ}\sin 108^{\large\circ}\sin 144^{\large\circ}$ is equal to

asked Oct 16, 2013 by sreemathi.v

1 answer

If $\sin\alpha\sin\beta+1=0$ .Find $1+\cot \alpha\tan\beta=0$

asked Oct 16, 2013 by sreemathi.v

1 answer

If $A$ and $B$ are positive acute angles and $\cos A=\large\frac{1}{7},$ $\cos B=\large\frac{13}{14}$ then find $A-B$

asked Oct 16, 2013 by sreemathi.v

1 answer