Question 1 :
The value of $\sin { \left( {{ 45 }}^{o} +\theta \right) } -\cos { \left( {{ 45 }}^{o} -\theta \right) } $ is
Question 3 :
If $(1 - \cos A)/2 = x$, then the value of $x$ is
Question 4 :
If $\displaystyle \tan \theta =1$ and $\sin \phi=\dfrac{1}{\sqrt{2}} $ then the value of $\displaystyle \cos \left ( \theta +\phi \right )$ is
Question 5 :
Find the range if $\left[ 2\sin { x } \right] +\left[ \cos { x } \right] =-3,$ then the range of the function $f\left( x \right) =\sin { x } +\sqrt { 3 } \cos { x } $ in $\left[ 0,2\pi \right] $ (where $[.]$ denotes the greatest integer function)
Question 6 :
The most general solution of $tan\theta =-1 \,\,\ and \,\,\,\ cos\theta = \dfrac{1}{\sqrt{2}}$ is
Question 7 :
If range of $f(x)=\cos x, x\in \left(\dfrac {-\pi}{3}, \dfrac {\pi}{6}\right)$ is $(a,b)$, then
Question 8 : <div>In $\Delta$ $ABC$ the sides opposite to angles $A, B, C$ are denoted by $a, b, c$ respectively.<br/></div>lf $A=3B$, then $\displaystyle \frac{a-b}{2b}$ is equal to<br/>
Question 10 :
If $\sin x - \cos x = 0$, then what is the value of $\sin^{4}x + \cos^{4}x$?
Question 13 :
In $\Delta$ABC, $B=45^o$, $C=120^o$, $a=40$cm, the length of the perpendicular from A on BC produced is?
Question 14 :
$\cos A.\cos \left( {{{60}^ \circ } - A} \right)\cos \left( {{{60}^ \circ } + A} \right) = $
Question 15 :
Choose the correct answer from the alternatives given :<br/>Maximum value of 24sin $\theta$ + 7cos $\theta$ is
Question 18 :
Let F(K)= $\left( {1 + \sin \frac{\pi }{{2k}}} \right)\left( {1 + \sin \left( {k - 1} \right)\frac{\pi }{{2k}}} \right)\left( {1 + \sin \left( {2k + 1} \right)\frac{\pi }{{2k}}} \right)\left( {1 + \sin \left( {3k - 1} \right)\frac{\pi }{{2k}}} \right)$ <br>The value of $F(1)+F(2)+F(3)$ is equal to
Question 21 :
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 23 :
Let $x+y$ being acute and if $\sin x.\cos y+\cos x.\sin y=0$ then the value of $\sin x+\sin y=$
Question 25 :
The given expression is $\displaystyle \sin { \theta } \cos { \left( { 90 }^{ o }-\theta \right) } +\cos { \theta } \sin { \left( { 90 }^{ o }-\theta \right) } +4 $ equal to :<br/>
Question 26 :
Given that A is positive acute angle and $ { sin }^{ }A=\dfrac { \sqrt { 3 } -1 }{ 2 } ,$ then A take the value (s)-
Question 28 :
If $0^{\circ} \leq \theta \leq 90^{\circ}$ and $\sqrt{2} tan \theta - sec \theta =0$, then the value of $(\sqrt{2} sin \theta + 2 tan \theta)$ is -<br>
Question 30 :
In a triangle $ABC$, if $\sin { A } \sin { B } =\dfrac { ab }{ { c }^{ 2 } } $, then the triangle is
Question 31 :
If $\tan 45^{\circ} = \cot \theta$, then the value of $\theta$, in radians is
Question 32 : In $\Delta$ $ABC$ the sides opposite to angles $A, B, C$ are denoted by $a, b, c$ respectively, <div>then $\ \displaystyle \frac{b\cos A+a\cos B}{\cos C}$ is equal to<br/></div>
Question 33 :
Evaluate $8 \sqrt{3} \, \text{cosec}^2 30^o \, \sin \, 60^o \, \cos \, 60^o \, \cos^2 45^o \, \sin \, 45^o \, \tan \, 30^o \, \text{cosec}^3 45^o$
Question 36 :
$\cos { \left( \dfrac { 3\pi }{ 4 } +x \right) } -\cos { \left( \dfrac { 3\pi }{ 4 } -x \right) } =\sqrt { 2 } .\sin { x }$<br/>
Question 38 :
If $\tan { \theta }$ =$\dfrac{-4}{3}$ then $\sin { \theta } $ is
Question 39 :
If $\displaystyle \tan { \theta } =\frac { 1 }{ 2 } $ and $\displaystyle \tan { \phi } =\frac { 1 }{ 3 } $, then the value of $\displaystyle \theta +\phi $ is:
