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Recent questions tagged ch3

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

If $\cot\theta+\tan\theta=2cosec \theta$,then find the general value of $\theta$

asked Apr 18, 2014 by sreemathi.v

1 answer

Find the most general value of $\theta$ satisfying the equation $\tan\theta=-1$ and $\cos \theta=\large\frac{1}{\sqrt 2}$

asked Apr 18, 2014 by sreemathi.v

1 answer

If $\tan \theta=\large\frac{\sin \alpha-\cos\alpha}{\sin \alpha+\cos\alpha}$ then show that $\sin\alpha+\cos\alpha=\sqrt 2\cos\theta$

asked Apr 18, 2014 by sreemathi.v

1 answer

If $\large\frac{\sin(x+y)}{\sin(x-y)}=\frac{a+b}{a-b}$ then show that $\large\frac{\tan x}{\tan y}=\frac{a}{b}$

asked Apr 18, 2014 by sreemathi.v

1 answer

If $\cos\alpha+\cos\beta=0=\sin\alpha+\sin \beta$,then prove that $\cos 2\alpha+\cos 2\beta=-2\cos(\alpha+\beta)$

asked Apr 18, 2014 by sreemathi.v

1 answer

If $\tan(A+B)=p$ and $\tan(A-B)=q$ then show that $\tan 2A=\large\frac{p+q}{1-pq}$

asked Apr 18, 2014 by sreemathi.v

1 answer

If $\tan \theta+\sin \theta=m$ and $\tan\theta-\sin \theta=n$ then prove that $m^2-n^2=4\sin \theta\tan\theta$

asked Apr 18, 2014 by sreemathi.v

1 answer

Prove that $\sin 4A=4\sin A\cos^3A-4\cos A\sin^3A$

asked Apr 18, 2014 by sreemathi.v

1 answer

Find the value of $\tan 22^{\large\circ}30'$

asked Apr 18, 2014 by sreemathi.v

1 answer

If $a\cos\theta+b\sin \theta=m$ and $a\sin \theta-b\cos\theta=n$ then show that $a^2+b^2=m^2+n^2$

asked Apr 18, 2014 by sreemathi.v

1 answer

If $\tan x=\large\frac{b}{a}$,then find the value of $\sqrt{\large\frac{a+b}{a-b}}+\sqrt{\frac{a-b}{a+b}}$

asked Apr 18, 2014 by sreemathi.v

1 answer

If $\cos(\alpha+\beta)=\large\frac{4}{5}$ and $\sin (\alpha-\beta)=\large\frac{5}{13}$ where $\alpha$ lies between $0$ and $\large\frac{\pi}{4}$,find the value of $\tan 2\alpha$

asked Apr 18, 2014 by sreemathi.v

1 answer

If $m\sin \theta=n\sin(\theta+2\alpha)$,then prove that $\tan(\theta+\alpha)\cot\alpha=\large\frac{m+n}{m-n}$

asked Apr 18, 2014 by sreemathi.v

1 answer

If $\large\frac{2\sin \alpha}{1+\cos \alpha+\sin \alpha}$$=y$,then prove that $\large\frac{1-\cos \alpha+\sin \alpha}{1+\sin \alpha}$ is equal to $y$

asked Apr 18, 2014 by sreemathi.v

1 answer

Prove that $\large\frac{\tan A+\sec A-1}{\tan A-\sec A+1}=\frac{1+\sin A}{\cos A}$

asked Apr 18, 2014 by sreemathi.v

1 answer

Find $\sin \large\frac{x}{2},$$\cos \large\frac{x}{2}$ and $\tan \large\frac{x}{2}$ when $\cos x=-\large\frac{1}{3}$.$x$ in quadrant III

asked Apr 18, 2014 by sreemathi.v

1 answer

Find $\sin \large\frac{x}{2},$$\cos \large\frac{x}{2}$ and $\tan \large\frac{x}{2}$ when $\tan x=-\large\frac{4}{3}$,$x$ in quadrant II

asked Apr 18, 2014 by sreemathi.v

1 answer

Evaluate $\sin 3x+\sin 2x-\sin x=4\sin x\cos\large\frac{x}{2}$$\cos\large\frac{3x}{2}$

asked Apr 18, 2014 by sreemathi.v

1 answer

Prove that $\large\frac{(\sin 7x+\sin 5x)+(\sin 9x+\sin 3x)}{(\cos 7x+\cos 5x)+(\cos 9x+\cos 3x)}$$=\tan 6x$

asked Apr 18, 2014 by sreemathi.v

1 answer

Evaluate $\sin x+\sin 3x+\sin 5x+\sin 7x$

asked Apr 18, 2014 by sreemathi.v

1 answer

Prove that $(\cos x-\cos y)^2+(\sin x-\sin y)^2=4\sin^2\large\frac{x-y}{2}$

asked Apr 18, 2014 by sreemathi.v

1 answer

Evaluate: $(\cos x+\cos y)^2+(\sin x-\sin y)^2$

asked Apr 18, 2014 by sreemathi.v

1 answer

Prove that $(\sin 3x+\sin x)\sin x+(\cos 3x-\cos x)\cos x=0$

asked Apr 18, 2014 by sreemathi.v

1 answer

Evaluate:$2\cos\large\frac{\pi}{13}$$\cos \large\frac{9\pi}{13}+$$\cos \large\frac{3\pi}{13}$$+\cos \large\frac{5\pi}{13}$

asked Apr 18, 2014 by sreemathi.v

1 answer

Find the general solution for the equation $\sin x+\sin 3x+\sin 5x=0$

asked Apr 18, 2014 by sreemathi.v

1 answer

Find the general solution for each of the following equation $\sec^22x=1-\tan 2x$

asked Apr 18, 2014 by sreemathi.v

1 answer

Find the general solution for the equation $\sin 2x+\cos x=0$

asked Apr 18, 2014 by sreemathi.v

1 answer

Find the general solution for the equation $\cos 3x+\cos x-\cos 2x=0$

asked Apr 18, 2014 by sreemathi.v

1 answer

Find the general solution for each of the following equation $\cos 4x=\cos 2x$

asked Apr 18, 2014 by sreemathi.v

1 answer

Find the principal and general solution for the equation $cosec x=-2$

asked Apr 17, 2014 by sreemathi.v

1 answer

Find the principal and general solution for the equation $\cot x=-\sqrt 3$

asked Apr 17, 2014 by sreemathi.v

1 answer

Find the principal and general solution for the equation $\sec x= 2$

asked Apr 17, 2014 by sreemathi.v

1 answer

Find the principal and general solution of the following equation $\tan x=\sqrt 3$

asked Apr 17, 2014 by sreemathi.v

1 answer

Prove :$\cos 6x=32\cos ^6x-48\cos^4x+18\cos^2x-1$

asked Apr 17, 2014 by sreemathi.v

1 answer

Prove : $\cos 4x=1-8\sin^2x\cos^2x$

asked Apr 17, 2014 by sreemathi.v

1 answer

Prove : $\tan 4x=\large\frac{4\tan x(1-\tan^2x)}{1-6\tan^2x+\tan^4x}$

asked Apr 17, 2014 by sreemathi.v

1 answer

Prove : $\cot x\cot 2x-\cot 2x\cot 3x-\cot 3x.\cot x$=1

asked Apr 17, 2014 by sreemathi.v

1 answer

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