Recent questions tagged medium

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

The interval in which $x$ must lie so that the greatest term in the expansion of $(1+x)^{2n}$, ($x>0$) has greatest coefficient is

asked Oct 16, 2013 by rvidyagovindarajan_1

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

If $p$ and $q$ are +ve real numbers such that $p^2+q^2=1$ then the maximum value of $(p+q)$ is

asked Oct 16, 2013 by sreemathi.v

1 answer

The number of real solutions of $\tan^{-1}\sqrt{x(x+1)}+\sin^{-1}\sqrt{x^2+x+1}=\large\frac{\pi}{2}$ is

asked Oct 15, 2013 by sreemathi.v

1 answer

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

asked Oct 15, 2013 by sreemathi.v

1 answer

The maximum value of the expression $\large\frac{1}{\sin^2\theta+3\sin\theta\cos\theta+5\cos^2\theta}$ is

asked Oct 15, 2013 by sreemathi.v

1 answer

If $\cos(\theta-\alpha)=a$ and $\sin(\theta-\beta)=b$ then $\cos^2(\alpha-\beta)+2ab\sin(\alpha-\beta)$ is equal to

asked Oct 15, 2013 by sreemathi.v

1 answer

If in a $\Delta$ le $ABC,A=\large\frac{\pi}{4}$ and $\tan B\tan C=\alpha$ then the value of $\alpha$ lies in

asked Oct 15, 2013 by sreemathi.v

1 answer

If $\sqrt{a+b}\tan\large\frac{\theta}{2}$$=\sqrt{a-b}\tan\large\frac{ \phi}{2}$ then $(b-a\sec \theta)(b+a\cos\phi)$ has maximum value $\lambda$ then $\lambda$ is

asked Oct 15, 2013 by sreemathi.v

1 answer

The expression $P(x)$ = $\big(\sqrt {x^5-1}+x\big)^7$ - $\big(\sqrt {x^5-1}-x\big)^7$ is a polynomial of what degree?

asked Oct 15, 2013 by rvidyagovindarajan_1

1 answer

$\cos\large\frac{\pi}{11}$$\cos\large\frac{2\pi}{11}$$\cos\large\frac{3\pi}{11}..........$$\cos\large\frac{11\pi}{11}$ is equal to

asked Oct 15, 2013 by sreemathi.v

1 answer

If $a\cos 2\theta+b\sin 2\theta=c$ has $\alpha$ & $\beta$ as its solutions then $\tan\alpha+\tan\beta$ and $\tan\alpha\tan\beta$ is equal to

asked Oct 15, 2013 by sreemathi.v

1 answer

Let $f(x)=\cos x(\sin x+\sqrt{\sin^2 x+\sin^2\theta})$ where $\theta$ is a given constant then maximum value of $f(x)$ is

asked Oct 15, 2013 by sreemathi.v

1 answer

If $\sin\alpha\sin\beta-\cos\alpha\cos\beta+1=0$ then the value of $\cot\alpha\tan\beta$ is

asked Oct 15, 2013 by sreemathi.v

1 answer

If $\alpha,\beta,\gamma,\delta$ are the solutions of the equation $\tan\big(\theta+\large\frac{\pi}{4}\big)=$$3\tan 3\theta$,no two of which have equal tangents,then the value of $\tan\alpha+\tan\beta+\tan\gamma+\tan\delta$ is equal to

asked Oct 15, 2013 by sreemathi.v

1 answer

If $\cos A=m\cos B$ and $\cot\large\frac{A+B}{2}$$=\lambda\tan\large\frac{B-A}{2}$ then $\lambda$ is

asked Oct 15, 2013 by sreemathi.v

1 answer

If $x\in(\pi,2\pi)$ and $\large\frac{\sqrt{1+\cos x}+\sqrt{1-\cos x}}{\sqrt{1+\cos x}-\sqrt{1-\cos x}}$$=\cot\big(a+\large\frac{x}{2}\big)$ then $'a'$ is equal to

asked Oct 15, 2013 by sreemathi.v

1 answer