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Questions >> JEEMAIN and NEET >> Mathematics >> Trigonometry

consider the equation sec θ+cosec θ=a, θ ∈(0,2π)-{ π/2, π,3π/2}

asked Jul 4, 2015 by excellentdeals18

0 answers

For a $\Delta ABC$ it is given that : $\cos A+\cos B+\cos C=\large\frac{3}{2}$ .What type of triangle is $ABC$ ?

asked Nov 19, 2013 by sreemathi.v

1 answer

If $0\leq x\leq \large\frac{\pi}{2}$ and $81^{\large \sin^2x}+81^{\large\cos^2x}=30$ then $x$ is equal to

asked Nov 19, 2013 by sreemathi.v

1 answer

Total number of solutions of $\cos x.\cos 2x.\cos 3x=\large\frac{1}{4}$ in $[0,\pi]$ is equal to

asked Nov 19, 2013 by sreemathi.v

1 answer

If $\tan^{-1}(x-1)+\tan^{-1}x+\tan^{-1}(x+1)=\tan^{-1}3x$ then $x$ is

asked Nov 19, 2013 by sreemathi.v

1 answer

If $\cos^{-1}x-\cos^{-1}\large\frac{y}{2}$ $=\alpha$ then $4x^2-4xy.\cos \alpha-y^2$ is equal to

asked Nov 19, 2013 by sreemathi.v

1 answer

Solve : $\log _7\log _5(\sqrt{x+5}+\sqrt{x})=0$

asked Nov 19, 2013 by sreemathi.v

1 answer

If $x>1,y>1,z>1$ are in G.P then $\large\frac{1}{1+ln\; x},\frac{1}{1+ln\; y},\frac{1}{1+ln \;z}$ are in

asked Nov 19, 2013 by sreemathi.v

1 answer

Let $ABCD$ be a quadrilateral with area 18 with side AB parallel to the side CD and AB=2CD.Let AD be $\perp$ to AB and CD.If a circle is drawn inside the quadrilateral ABCD touching all the sides then its radius is

asked Nov 19, 2013 by sreemathi.v

1 answer

The radius of the circle passing through the centre of the inscribed circle of the $\Delta$ le ABC and through the end point of the base BC is R then $\large\frac{a}{R}$ $\sec \large\frac{A}{2}$ is equal to

asked Nov 18, 2013 by sreemathi.v

1 answer

$ABC$ is a $\Delta$ le.Its area is 12sqcm and base is 6cm.The difference of base angle is $60^{\large\circ}$ .If $A$ be the angle opposite to the base,then the value of $8\sin A-6\cos A$ is

asked Nov 18, 2013 by sreemathi.v

1 answer

The number of all possible values of $\theta$ where $0 < \theta < \pi$ for which the system of equations $(y+z)\cos 3\theta=(xyz)\sin 3\theta$ , $x\sin 3\theta=\large\frac{2\cos 3\theta}{y}+\frac{2\sin 3\theta}{z}$ , $(xyz)\sin 3\theta=(y+2z)\cos 3\theta+y\sin 3\theta$ have a solution $(x_0,y_0,z_0)$ with $y_0,z_0\neq 0$ is

asked Nov 18, 2013 by sreemathi.v

1 answer

The positive integer value of $n>3$ satisfying the equation $\large\frac{1}{\sin\big(\Large\frac{\pi}{n}\big)}=\frac{1}{\sin\big(\Large\frac{2\pi}{n}\big)}+\frac{1}{\sin\big(\Large\frac{3\pi}{n}\big)}$ is

asked Nov 18, 2013 by sreemathi.v

1 answer

If $\sin^{-1}\big(x-\large\frac{x^2}{2}+\frac{x^3}{4}-........)$ $+\cos^{-1}(x^2-\large\frac{x^4}{2}+\frac{x^6}{4}.......)=\large\frac{\pi}{2}$ .For $0<\mid x\mid<\sqrt 2$ then $x$ equals

asked Nov 18, 2013 by sreemathi.v

1 answer

Find all positive integral solutions of the equation $\tan^{-1}x+\cot^{-1}y=\tan^{-1}3$

asked Nov 18, 2013 by sreemathi.v

1 answer

Let $ABC$ be a triangle such that $\angle ACB=\large\frac{\pi}{6}$ .Let $a,b$ and $c$ denote the lengths of the sides opposite to $A,B$ and $C$ respectively.The value of $x$ for which $a=x^2+x+1,b=x^2-1$ and $c=2x+1$ is

asked Nov 18, 2013 by sreemathi.v

1 answer

Two sides of a $\Delta$ le are given by the roots of the equation $x^2-2\sqrt 3x+2=0$ ,The angle between the sides is $\large\frac{\pi}{3}$ .The perimeter of the triangle is

asked Nov 18, 2013 by sreemathi.v

1 answer

Find the maximum and minimum value of $\sin^6x+\cos^6x$

asked Nov 18, 2013 by sreemathi.v

1 answer

The value of $x$ where $d>0$ and $\tan[\sec^{-1}\big(\large\frac{1}{x}\big)]=$ $\sin(\tan^{-1}2)$ is

asked Nov 18, 2013 by sreemathi.v

1 answer

If $\cot^{-1}(\sqrt{\cos\alpha})-\tan^{-1}(\sqrt{\cos\alpha})=x$ then $\sin x$ is equal to

asked Nov 18, 2013 by sreemathi.v

1 answer

$ABC$ is a triangle with $\angle A=30^{\large\circ}$ $BC=10$ cm.The area of the circumcircle of the $\Delta$ le is?

asked Nov 18, 2013 by sreemathi.v

1 answer

The circumradius of the $\Delta$ le whose sides are $13,12\; and\; 5 \;is$ ?

asked Nov 18, 2013 by sreemathi.v

1 answer

Two sides of $\Delta$ le are $\sqrt 2-1$ and $\sqrt 2+1$ unit and their included angle is $60^{\large\circ}$ .Then the third side of the $\Delta$ le is

asked Nov 18, 2013 by sreemathi.v

1 answer

The number of values of $x$ in $[0,2\pi]$ satisfying the equation $3\cos 2x-10\cos x+7=0$ is?

asked Nov 18, 2013 by sreemathi.v

1 answer

The solution of the equation $4\sin^4x+\cos^4x=1$ is

asked Nov 18, 2013 by sreemathi.v

1 answer

The number of values of $x$ in the interval $[0,3\pi]$ .Satisfying the equation $2\sin^2x+5\sin x-3=0$ is

asked Nov 18, 2013 by sreemathi.v

1 answer

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

asked Nov 15, 2013 by sreemathi.v

1 answer

If $x\sin^3\theta+y\cos^3\theta=\sin\theta\cos\theta$ and $x\sin\theta=y\cos\theta$ then $x^2+y^2$ is

asked Nov 15, 2013 by sreemathi.v

1 answer

The solution of the equation $[\sin x+\cos x]^{1+\sin 2x}=2,-\pi\leq x\leq \pi$ is

asked Nov 15, 2013 by sreemathi.v

1 answer

If $\sec\theta=m$ and $\tan\theta=n$ then $\large\frac{1}{m}$ $\big[(m+n)+\large\frac{1}{(m+n)}\big]$

asked Nov 15, 2013 by sreemathi.v

1 answer

In a $\Delta ABC$ if $b=2,B=30^{\large\circ}$ then the area of the circumcircle of $\Delta$ ABC in square unit is

asked Nov 15, 2013 by sreemathi.v

1 answer

In a $\Delta$ ABC if the sides are $a=3,b=5,c=4$ then $\sin\large\frac{B}{2}$ $+\cos{\large\frac{B}{2}}$ is equal to

asked Nov 15, 2013 by sreemathi.v

1 answer

The sides of a $\Delta$ le are respectively 7cm, $4\sqrt 3$ cm and $\sqrt{13}$ cm then the smallest angle of the triangle is

asked Nov 15, 2013 by sreemathi.v

1 answer

Solve for $x$ : $\tan^{-1}x+2\cot^{-1}x=\large\frac{2\pi}{3}$ .

asked Nov 15, 2013 by sreemathi.v

1 answer

If $-\large\frac{x}{2}$ $<\sin^{-1}x<\large\frac{x}{2}$ then $\tan(\sin^{-1}x)$ is equal to

asked Nov 15, 2013 by sreemathi.v

1 answer

If $\tan^{-1}\big(\large\frac{a}{x}\big)$ $+\tan^{-1}\big(\large\frac{b}{x}\big)=\frac{\pi}{2}$ then $x$ is equal to

asked Nov 15, 2013 by sreemathi.v

1 answer

If $\tan^{-1}\large\frac{1}{a-1}$ $=\tan^{-1}x+\tan^{-1}(x+1)=\tan^{-1}3x$ is

asked Nov 15, 2013 by sreemathi.v

1 answer

If in any $\Delta ABC$ $A=30^{\large \circ}$ and $B=60^{\large\circ}$ then find $a: b:c$

asked Nov 15, 2013 by sreemathi.v

1 answer

Find all possible values of $p$ and $q$ for which $\cos^{-1}\sqrt p+\cos^{-1}\sqrt{1-p}=\large\frac{3\pi}{4}$

asked Oct 21, 2013 by sreemathi.v

1 answer

The radii $r_1,r_2,r_3$ of described circle of a $\Delta$ le ABC are in harmonic progression.If its area is 24sq .cm,and its perimeter is 24,find the lengths of its sides

asked Oct 21, 2013 by sreemathi.v

1 answer

The greater of the angles $A=2\tan^{-1}(2\sqrt 2-1),B=3\sin^{-1}\big(\large\frac{1}{3}\big)$ $+\sin^{-1}(\large\frac{3}{5})$ is

asked Oct 21, 2013 by sreemathi.v

1 answer

Let $f(x) =x^2$ and $g(x)=\sin x$ for all $x\in R$ .Then the set of all $x$ satisfying $(fogogof)(x)=(gogof)(x)$ where $fog(x)=f(g(x))$ is

asked Oct 21, 2013 by sreemathi.v

1 answer

The sides of a $\Delta$ le are three consecutive natural numbers and its largest angle is twice the smallest one.Determine the sides of the triangle

asked Oct 21, 2013 by sreemathi.v

1 answer

The angles $A,B$ and $C$ of a triangle ABC are in arithmetic progression.If $2b^2=3C^2$ determine the angle A

asked Oct 21, 2013 by sreemathi.v

1 answer

Let $a,b,c$ be positive real numbers .Let $\theta=\tan^{-1}\sqrt{\large\frac{a(a+b+c)}{bc}}+$ $\tan^{-1}\sqrt{\large\frac{b(a+b+c)}{ca}}$ $+\tan^{-1}\sqrt{\large\frac{c(a+b+c)}{ab}}$ .Then $\tan\theta$

asked Oct 21, 2013 by sreemathi.v

1 answer

The value of the expression $\large\frac{\sin^3x}{1+\cos x}+\frac{\cos^3x}{1-\sin x}$ is

asked Oct 21, 2013 by sreemathi.v

1 answer

If $A+B+C=\pi$ then $\cos^2A+\cos^2B+\cos^2C$ is equal to

asked Oct 21, 2013 by sreemathi.v

1 answer

The value of $\sum\limits_{n=1}^{\infty}\large\frac{\tan\bigg(\Large\frac{\theta}{2^n}\bigg)}{2^{n-1}\cos\bigg(\Large\frac{\theta}{2^{n-1}}\bigg)}$ is equal to

asked Oct 18, 2013 by sreemathi.v

1 answer

If $A+B+C=\pi$ then $\sin 2A+\sin 2B-\sin 2C$ is equal to

asked Oct 18, 2013 by sreemathi.v

1 answer

If $A+B+C=\pi$ then the value of $\sin\large\frac{A}{2}$ $+\sin\large\frac{B}{2}$ $+\sin\large\frac{C}{2}$ is equal to

asked Oct 18, 2013 by sreemathi.v

1 answer

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