Question 1 :
If $\theta$ increases from $0^0$ to $90^o$, then the value of $\cos\theta$: <br/>
Question 2 :
$\tan \theta$ increases as $\theta$ increases.<br/>If true then enter $1$ and if false then enter $0$.<br/>
Question 3 :
If $\theta$ lies in the first quadrant and $5 \tan \theta = 4$, find $\displaystyle \frac{5 \sin \theta - 3 \cos \theta}{\sin \theta + 2 \cos \theta}$
Question 4 :
If $4\tan \theta = 3$, then $\dfrac {5\sin \theta + 3\cos \theta}{5\sin \theta - 3\cos \theta} = $
Question 7 :
If $A+B+C=\dfrac { 3\pi }{ 2 } $, then $cos2A+cos2B+cos2C$ is equal to
Question 8 :
$\dfrac{{\cos 17^\circ + \sin 17^\circ }}{{\cos 17^\circ - \sin 17^\circ }}$
Question 9 :
If $ \alpha \epsilon \left[ \frac { \pi }{ 2 } ,\pi \right] $ then the value of $\sqrt { 1+sin\alpha } -\sqrt { 1-sin\alpha } $ is equal to
Question 11 :
A ladder 20 m long is placed against a vertical wall of height 10 m, determine the distance between foot of the ladder and the wall and also the inclination of the ladder with the horizontal.
Question 12 :
If $\displaystyle \theta =45$ then $\displaystyle \frac { 2\tan { \theta } }{ 1+{ \tan }^{ 2 }\theta } $ is :
Question 13 :
$\displaystyle \sin { \theta } +\cos { \theta } =1$ where $\displaystyle \theta= $
Question 14 :
If $\tan \theta = \dfrac {4}{3}$ then $\cos \theta$ will be
Question 15 :
If $\sin\alpha + \sin\beta = a$ and $\cos \alpha - \cos \beta =b, $ then $\tan \left( \frac{\alpha -\beta}{2} \right) $ is equal to-
Question 16 :
$\sin { { 24 }^{ 0 } } +\sin { { 32 }^{ 0 } } +\sin { { 204 }^{ 0 } } +\sin { { 212 }^{ 0 } } =$
Question 17 :
The value of $\cos ^{ 2 }{ 73 }^{o} +\cos ^{ 2 }{ 47 }^{o} -\sin ^{ 2 }{ 43 }^{o} +\sin ^{ 2 }{ 107 }^{o}$ is equal to :
Question 19 : <div>Solve:</div>$\displaystyle \sin ^{4}\theta +2\cos ^{2}\theta \left ( 1-\frac{1}{\sec ^{2}\theta } \right )+\cos ^{4}\theta $
Question 21 :
If $cosec\,\theta=\dfrac{29}{21}$ where $0 < \theta < 90^0$, then what is the value of $4\sec\theta+4\tan\theta$ ?
Question 22 :
<span>If $\tan\alpha=\dfrac{4}{15} (0 < \alpha < 90^{\circ})$, then the value of $\displaystyle \frac{5 \sin \alpha + 7 \cos \alpha}{6 \cos\alpha - 3 \sin\alpha}$</span><br/>
Question 23 :
If $\displaystyle \tan { \theta } =\frac { 10 }{ 24 } $, then $\displaystyle \sin { \theta } $ is equal to :
Question 24 :
If $\displaystyle \sin \theta +\sin ^{2}\theta =1$ then the value of $\displaystyle \left ( \cos ^{2}\theta +\cos ^{4}\theta \right )$ is
Question 25 :
Which of the following is equal to $\sin x \sec x$?
Question 26 :
If $\displaystyle \cot A=\frac{12}{5}$ then the value of $\displaystyle \left ( \sin A+\cos A \right )$ $\displaystyle \times cosec$ $\displaystyle A$ is
Question 30 :
If $\displaystyle \cos \theta =\frac{1}{2}$ then the value of $\displaystyle \frac{2\sec \theta }{1+\tan ^{2}\theta }$ is
Question 31 :
$\dfrac { cos20{ }^{ \circ }+8sin70{ }^{ \circ }sin50{ }^{ \circ }sin10{ }^{ \circ } }{ { sin }^{ 2 }80{ }^{ \circ } } $ is equal to
Question 32 :
If $\displaystyle \sin { x } +{ \sin }^{ 2 }x=1$, then $\displaystyle { \cos }^{ 12 }x+3{ \cos }^{ 10 }x+3{ \cos }^{ 8 }x+{ \cos }^{ 6 }x$ is equal to:
Question 33 :
If sin $\left (A-B \right )= \dfrac {1}{2}$ and cos$\left ( A+B\right) = \dfrac {1}{2}$, then the value of B is :<br/>
Question 34 :
If in a triangle $ABC, 2 \cos A = \sin B \,cosec \,C$, then
Question 35 :
If $x = \cos 10 ^ { \circ } \cos 20 ^ { \circ } \cos 40 ^ { \circ } $ then $x$ equals to
Question 36 :
Consider the following statements:<br/>(1) The value of $\cos { { 46 }^{ o } } -\sin { { 46 }^{ o } } $ is positive.<br/>(2) The value of $\cos { { 44 }^{ o } } -\sin { { 44 }^{ o } } $ is negative<br/>Which of the above statements is/are correct?
Question 37 :
Let $\theta \in \left( {0,{\pi \over 4}} \right)$ and ${t_1} = {\left( {\tan \theta } \right)^{\tan \theta }}$, ${t_2} = {\left( {\tan \theta } \right)^{\cot \theta }}$, ${t_3} = {\left( {\cot \theta } \right)^{\tan \theta }}$ then ${t_4} = {\left( {\cot \theta } \right)^{\cot \theta }}$, then
Question 38 :
The value of $x$ for which the tangents to the curves $y = x \cos{x}, \ y = \dfrac{\left(\sin{x} \right)}{ x}$ are parallel to the axis of $x$ are roots of
Question 39 :
The value of $\displaystyle \left ( \sin A-\cos A \right )^{2}+\left ( \sin A+\cos A \right )^{2}$ is _____
Question 40 :
What is the value of $\sec^2 (\tan^{-1} ( \frac {5}{11} )) $ ?
Question 41 :
Assertion: In a right angled triangle, if $\tan \theta =\frac{3}{4}$, the greatest side of the triangle is 5 units.
Reason: $(greatest \:side)^2=(hypotenuse)^2$<br> $\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \;\; \; \; =(perpendicular)^2+(base)^2$
Question 42 :
If sin A= $\dfrac{1}{2}$, then the value of cot A is<br/><br/>
Question 44 :
If $\dfrac{1+\sin 2x}{1-\sin 2x}=\cot ^2\left ( a+x \right )\forall\ x\ \in\ R\sim \left ( n\pi +\dfrac{\pi }{4} \right ),n\ \in\ N,$ then a can be
Question 46 :
$\sqrt { 2+\sqrt { 2+\sqrt { 2+\sqrt { 2 }} } } =$
Question 47 :
If $\sin { \theta } +\cos { \theta } =0$ and $0<\theta <\pi $, then $\theta$
Question 48 :
If $\displaystyle \sin A=\frac{\sqrt{3}}{2}$ and A is an acute angle, then find the value of $\displaystyle \frac{\tan A-\cot A}{\sqrt{3}+co\sec A}$
Question 51 :
In $\triangle ABC$, right angled at $B$, $AB = 24\space cm, BC = 7\space cm$. Determine$:(i)\space \sin A, \cos A, \space (ii)\space \sin C, \cos C$
Question 52 :
If $0\leq x, y\leq 180^o$ and $\sin (x-y)=\cos(x+y)=\dfrac 12$, then the values of $x$ and $y$ are given by
Question 53 :
If $\displaystyle \sin^4\theta+\frac {1}{\sin^4\theta}=194$, then the value of $(2 \text{cosec}\theta-\cot\theta \cos\theta)$ can be<br/>
Question 55 :
If $\displaystyle \sin ^{4}\theta +\cos ^{4}\theta =\dfrac{1}{2} $ then the value of $\displaystyle \sin \theta \cos \theta $ is
