Question 1 :
If $\theta$ increases from $0^0$ to $90^o$, then the value of $\cos\theta$: <br/>
Question 3 :
The value of $\cos ^{ 2 }{ 73 }^{o} +\cos ^{ 2 }{ 47 }^{o} -\sin ^{ 2 }{ 43 }^{o} +\sin ^{ 2 }{ 107 }^{o}$ is equal to :
Question 4 :
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 5 :
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 6 :
Which of the following is equal to $\sin x \sec x$?
Question 9 :
<div>Solve:</div>$\displaystyle \sin ^{4}\theta +2\cos ^{2}\theta \left ( 1-\frac{1}{\sec ^{2}\theta } \right )+\cos ^{4}\theta $
Question 10 :
If $A+B+C=\dfrac { 3\pi }{ 2 } $, then $cos2A+cos2B+cos2C$ is equal to
Question 11 :
The simplified value of $\displaystyle \left ( \frac{1-\sin \alpha }{\cos \alpha }+\frac{\cos \alpha }{1+\sin \alpha } \right )\left ( \sec \alpha +\frac{1}{\cot \alpha } \right )$ is _____<br/>
Question 13 :
<p>If $ \tan \left( {\cot x} \right) = \cot \left( {\tan<br/>x} \right),$ then</p>
Question 14 :
If a line in the space makes angle $a, p$ and $y$ with the coordinate axes, then<br/>$\cos\,2a\,+\cos\,2b\,+\,\cos\,2y\,+\,\sin^2\,a\,+\,\sin^2\beta\,+\,\sin^2\,y\,$ equals
Question 15 :
$\displaystyle \sec ^{4}\theta -\sec ^{2}\theta $ in terms of $\displaystyle \tan \theta $ is ___
Question 18 :
If $\cos\theta = \dfrac{2}{21}$ and $\sin\theta = \dfrac{6}{7}$, what is the value of $\tan\theta$?<br/>
Question 19 :
In a $\triangle ABC,\ I$ is the incentre. The ratio $IA :IB:IC$ is equal to
Question 21 :
If $2 \sec 2\alpha = \tan\beta + \cot \beta$, then one of the value of $\alpha+\beta$ is-
Question 22 :
Assertion: If $\displaystyle \sin \theta + co\sec \displaystyle \theta =2,$ then $\displaystyle \sin ^{n}\theta + co\sec\displaystyle ^{n}\theta =2^{n}\cdot $
Reason: If $a+b=2$, $ab=1$, then $a=b=1$.
Question 23 :
If $\displaystyle \sin ^{4}\theta +\cos ^{4}\theta =\dfrac{1}{2} $ then the value of $\displaystyle \sin \theta \cos \theta $ is
Question 24 :
${\cos ^2}{48^ \circ } - {\sin ^2}{12^ \circ }$ is equal to -
Question 25 :
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