Question 1 :
If $\displaystyle \alpha +\beta =90^{\circ}$ and $ \alpha =2\beta $, then $ \cos ^{2}\alpha +\sin ^{2}\beta $ equals to
Question 4 :
If $\theta$ is in the first quadrant and cos $\theta=\frac{3}{5}$, then the value of $\dfrac{5 tan \theta -4cosec \theta}{5 sec\theta-4cot \theta}$ is<br/><br/>
Question 5 :
$\cos A.\cos \left( {{{60}^ \circ } - A} \right)\cos \left( {{{60}^ \circ } + A} \right) = $
Question 7 :
In a triangle $ABC$, if $\sin { A } \sin { B } =\dfrac { ab }{ { c }^{ 2 } } $, then the triangle is
Question 8 :
The sum of integral values of $'n'$ such that equation $\sin x (2\sin x+\cos x)=n$ has at least one real solution is ?
Question 9 :
$(m + 2) sin \theta + (2m - 1) cos \theta = 2m + 1$ is true if
Question 11 :
If $\tan { \theta } =3$ and $\theta$ lies in the third quadrant, then the value of $\sin { \theta } $ is
Question 13 :
Given that A is positive acute angle and $ { sin }^{ }A=\dfrac { \sqrt { 3 } -1 }{ 2 } ,$ then A take the value (s)-
Question 14 :
If ${\tan ^2}\theta = 2\,{\tan ^2}\phi + 1$, then the value of $\cos \,2\theta + {\sin ^2}\phi \,is$ is
Question 15 : <div>State True or False</div><div> $\cos 2{ A } =\cos ^{ 2 }{ A } -\sin ^{ 2 }{ A } $</div>
Question 16 :
Let $P$ be the relation defined on the set of all real numbers such that $P={(a,b)/\sec^{2}\ a-\tan^{2}\ b=1}$, then $P$ is
Question 18 :
If $\displaystyle 0^{0}\leq \theta \leq 90^{0}$, find the value of $\displaystyle \theta $ satisfying $\displaystyle 3\tan \theta +\cot \theta =5\text{cosec} \theta $
Question 19 :
What is the value of $\dfrac {(\cos 10^{o}+\sin 20^{o})}{(\cos 20^{o}-\sin 10^{o})}$?
Question 21 :
If $\displaystyle \theta \in \left ( 0,\frac{\pi }{2} \right )$, then the value of $\displaystyle \cos \left ( \theta -\frac{\pi }{4} \right )$ lies in the interval
Question 22 :
The value of $\displaystyle \cos { \left( { 40 }^{ o }+\theta \right) - } \sin { \left( { 50 }^{ o }-\theta \right) } +\frac { { \cos }^{ 2 }40^{ o }+{ \cos }^{ 2 }{ 50 }^{ o } }{ { \sin }^{ 2 }{ 40 }^{ o }+{ \sin }^{ 2 }{ 50 }^{ o } } $ is :
Question 23 :
Find the number of solutions of the equation ${(1 - 2cos\theta )^2} + {(tan\theta + \sqrt 3 )^2} = 0$ in interval $[0,2\pi ]$
Question 24 :
Find the value of $\displaystyle \cos { \left( { 90 }^{ o }-A \right) } \tan { \left( { 90 }^{ o }-A \right) } \sec { \left( { 90 }^{ o }-A \right) } $
Question 25 :
If ABC is a triangle in which $B = 45^o, C = 120^o$ and $a = 40$, the length of the perpendicular from A on BC produced is
Question 27 :
$\displaystyle \sin ^{2}\theta= \frac{(x+y)^{2}}{4xy}$, where $\displaystyle x \epsilon R,$ $\displaystyle y \epsilon R,$ gives real $\displaystyle \theta$ if and only if
Question 28 :
If $0< x\leq \cfrac {\pi}{2}$, then $(\sin x+ \text{cosec} x)$ is greater than or equal to
Question 29 :
The value of $\displaystyle \frac { \cot { { 50 }^{ o } } }{ \tan { { 40 }^{ o } } } $ is :
Question 30 :
Find which of the number of the form $(n\:\pi-tan^{-1}3)$, where $n\:\epsilon\:l$, are solution for $\displaystyle 12tan\:2x+\frac{\sqrt{10}}{cos\:x}+1=0$
Question 32 :
In a triangle $ABC$, if $a \cos^2\dfrac{C}{2}+c\cos^2\dfrac{A}{2}=\dfrac{3b}{2}$, then the sides of triangle are in
Question 34 :
Evaluate: $\displaystyle\frac{-\tan\theta \cot(90^o-\theta)+\sec\theta cosec(90^o-\theta)+\sin^235^o+\sin^255^o}{\tan 10^o\tan 20^o\tan 30^o \tan 70^o \tan 80^o}$.
Question 35 :
If $\displaystyle \cos \alpha +\cos \beta =0=\sin \alpha +\sin \beta $ then $\displaystyle \cos 2\alpha +\cos 2\beta $ is equal to
Question 37 :
If in a triangle ABC $\displaystyle \frac{2 cos A}{a} + \frac{cos B}{b} + \frac{2 cos C}{c} = \frac{a}{bc} + \frac{b}{ca}$ then
Question 38 : <p><span>If $\alpha, \beta, \gamma, \delta$ are the solutions of the<br/>equation $\tan\left (\theta + \frac{\pi} {4} \right ) = 3 \tan 3\theta$, no two of which have<br/>equal tangents</span></p><p>The value of $\frac{1} {\tan \alpha} + \frac{1} {\tan \beta} + \frac{1} {\tan \gamma} + \frac{1} {\tan \delta}$ is</p>
Question 40 : <div>State True or False</div><div>If $x+y+z=\pi/2$, then $\sin 2x+\sin 2y+\sin 2z=4\cos x\cos y\cos z$.<br/></div>
Question 41 :
Solve $\displaystyle 2log_{(sin\:x)}2log_{(sin^{2}x)}a=-1$ stating any condition on $'a'$ that may be required for the existence of the solution.
Question 42 :
Assertion: Statement 1: $\displaystyle \sin x= a$ where $\displaystyle -1< a< 0$ then for $\displaystyle x\epsilon [0,n\pi ]$ has $2(n-1)$ solutions $\displaystyle \forall n\epsilon N$
Reason: Statement 2: $\sin x$ takes value $a$ exactly two times when we take one complete rotation covering all the quadrant starting from $\displaystyle x= 0$
Question 43 :
In a triangle $ABC$, $\angle B < \angle C$ and the values of $B$ & $C$ satisfy the equation $2 tan x-k (1+tan^2x)=0$ where $(0 < k < 1)$. Then the measure of $\angle A$ is:
Question 44 :
The sum of all the solutions of the equation $\cos x.\cos \left ( \dfrac{\pi }{3}+x \right ).\cos \left ( \dfrac{\pi }{3}-x \right )=\dfrac{1}{4}, x\in \left [ 0, 6\pi \right ]$ is
Question 45 :
$1+{ }^nC_1 \cos \theta + { }^nC_2 \cos 2\theta + ........ + { }^nC_n \cos n\theta$ equals
Question 47 :
In a triangle, the lengths of the two larger sides are 10 and 9, respectively. If the angles are in A.P., the lengths of the third side can be
Question 48 :
Number of solution of the equation |sin x | = sin x + 2 cos x , in the interval $\displaystyle \left [ 0, 2\pi \right ]$
Question 49 :
If $\displaystyle 0\le x < 2\pi$, then the number of real values of $x,$ which satisfy the equation $\displaystyle \cos { x } +\cos { 2x } +\cos { 3x } +\cos { 4x } =0$:<br/>
Question 50 :
In a triangle $ABC$ if $\cot{A}={\left({x}^{3}+{x}^{2}+x\right)}^{\frac{1}{2}} , \cot{B}={\left({x}^{-1}+x+1\right)}^{\frac{1}{2}}$ and $ \cot{C}={\left({x}^{-3}+{x}^{-2}+{x}^{-1}\right)}^{\frac{-1}{2}}$ then the triangle is
Question 51 :
If $\alpha$ & $\beta $ satisfy the equation, $a\cos2\theta + b\sin\ 2\theta = c$ then $\displaystyle \cos^2\alpha + \cos^2\beta=$ <br>
Question 52 :
What is the simplified value of $\cfrac { \sin { 2A } }{ 1+\cos { 2A } } $?
Question 53 : Arrange the following values in the ascending order of their magnitudes <div><br/>A : lf $ A+B+C=\pi$ then</div><div><br/>$\displaystyle \frac{\cos A}{\sin B\sin C}+\frac{\cos B}{\sin A\sin C}+\frac{\cos C}{\sin A\sin B}=$<br/><br/>B : If $ A+B+C=\pi$ then $\displaystyle \sum\cot A.\ \cot B=$<br/><br/>C : If $ A+B+C=\pi$ then<br/>$<br/>\tan 3A+\tan 3B+\tan 3C=2K\tan 3A\tan 3B\tan 3C, then \ K=$<br/><br/>D : lf $ A+B+C=\pi$ then<br/>$\sec A(cosB\cos C-\sin B\sin C)=$<br/></div>
Question 55 :
In a triangle $ABC$, $\sin A\cos B=\dfrac{1}{4}$ and $3\tan A=\tan B$ , the triangle is
Question 56 :
Which of the following sets can be the subset of the general solution of $1 + \cos 3x = 2 \cos 2x (n \epsilon Z)$ ?
Question 57 :
If ${P_n} = {\cos ^n}\theta + {\sin ^n}\theta ,$ then $2{p_6} - 3{p_4} + 5 = ..........$
Question 59 :
If $\sin^{2}A=x$ , then $\sin A \sin 2A \sin 3A \sin 4A$ is a polynomial in $x$, the sum of whose coefficients is
Question 60 : If in a $\Delta ABC, \begin{vmatrix}\sin A\:\:\sin B\:\:\sin C \\ \sin B\:\:\sin C\:\:\sin A \\ \sin C\:\:\sin A\:\:\sin B\end{vmatrix}=0$<div>Then which of the following statement is True?</div>
