Trigonometry - Class XI
Comprehensive trigonometry quiz covering identities, equations, angle values, simplifications, and height and distance applications for Class XI curriculum
Questions
The value of ${ cosec }^{ 2 }{ 51 }^{ 0 }-{ cot }^{ 2 }{ 51 }^{ 0 }$ is
- 1
- -1
- 0
- $\frac { 1 }{ 2 } $
Choose the correct option for the following statement.
- The given statement is true
- The given statement is false
- Incomplete information
- None of the above.
$\sin { { 30 }^{ o }= } $
- $\dfrac {1}{2}$
- $-\dfrac {1}{2}$
- $\dfrac {\sqrt {3}}{2}$
- $-\dfrac {\sqrt {3}}{2}$
The value of $\tan 7\dfrac{1}{2}^{o}$ is equal to
- $\sqrt{6}+\sqrt{3}+\sqrt{2}-2$
- $\sqrt{6}-\sqrt{3}+\sqrt{2}-2$
- $\sqrt{6}-\sqrt{3}+\sqrt{2}+2$
- $\sqrt{6}-\sqrt{3}-\sqrt{2}-2$
General solution of $cotx+tanx=2cosecx$ is
- $2n\pi\pm\dfrac{2\pi}{3},n\inZ$
- $2n\pi\pm\dfrac{4\pi}{3},n\in Z$
- $2n\pi\pm\dfrac{5\pi}{3},n\in Z$
- $2n\pi\pm\dfrac{\pi}{3},n\in Z$
If $\cos A=\cos $ and $\sin A=\sin B$ then
- $A+B=0$
- $A=B$
- $A+B=2n \pi$
- $A=B+2n \pi$
$\left( 1-\dfrac { \cos { 61^{o} } }{ \cos { 1^{o} } } \right) \left( 1-\dfrac { \cos { 62^{o} } }{ \cos { 2^{o} } } \right) \left( 1-\dfrac { \cos { 63^{o} } }{ \cos { 3^{o} } } \right) .......\left( 1-\dfrac { \cos { 119^{o} } }{ \cos { 59^{o} } } \right) $
- $-1$
- $1$
- $2$
- $0$
If $\tan \theta =\dfrac {\cos 9^{o}+\sin 9^{o}}{\cos 9^{o}-\sin 9^{o}}$, then the value of $\theta$ is
- $9^{o}$
- $54^{o}$
- $18^{o}$
- $None\ of\ these$
The value of $\tan \theta .\tan (\theta +60^{o})+\tan \theta \tan (\theta -60^{o})+\tan (\theta +60^{o}).\tan (\theta -60^{o})+3$ is
- $0$
- $1$
- $-1$
- $None\ of\ these$
The value of $\sin 75^{o}$ is
- $\dfrac {2-\sqrt {3}}{\sqrt {2}}$
- $\dfrac {\sqrt {3}+1}{2\sqrt {2}}$
- $\dfrac {\sqrt {3}-1}{2\sqrt {2}}$
- $\dfrac {\sqrt {3}+1}{\sqrt {2}}$
If a=cos 2 and b=sin 7, then
- b>0
- ab<0
- a>b
- ab>0
$\dfrac{\cos{20}^{o}+8\sin{70}^{o}\sin{50}^{o}\sin{10}^{o}}{{\sin}^{2}{80}^{0}}$ is equal to:
- $1$
- $2$
- $\dfrac{3}{4}$
- $\none$
The value of expression $\dfrac { 2\left( \sin{ 1 }^{ o }+\sin{ 2 }^{ o }+\sin{ 3 }^{ o }+.....+\sin{ 89 }^{ o } \right) }{ 2\left( \cos{ 1 }^{ o }+\cos{ 2 }^{ o}+......+\cos{ 44 }^{ o } \right) +1 }$ equals
- $\sqrt{2}$
- $1/\sqrt{2}$
- $1/2$
- $0$
${\cos}^{2}{73}^{o}+{\cos}^{2}{47}^{o}+\cos{73}^{o}\cos{47}^{o}=.$
- $\dfrac{3}{4}$
- $-\dfrac{3}{4}$
- $\dfrac{4}{3}$
- $-\dfrac{4}{3}$
$\dfrac { \cos{ 13 }^{ o }-\sin{ 13 }^{ o } }{ \cos{ 13 }^{ o }+\sin{ 13 }^{ o } } +\dfrac { 1 }{ \cot{ 148 }^{ o } }$ is equal to
- $1$
- $-1$
- $0$
- $\dfrac { 1 }{ 2 } $
The value of $\sqrt { 3 } tan{ 10 }^{ 0 }+\sqrt { 3 } tan{ 20 }^{ 0 }+tan{ 10 }^{ 0 }tan{ 20 }^{ 0 }$ is ___________.
- $-1$
- $0$
- $1$
- $2$
If $sin(A-B)=\frac { 1 }{ 2 } ,cos(A+B)=\frac { 1 }{ 2 } ,{ 0 }^{ 0 }<A+B\le { 90 }^{ 0 }$ then A =
- $15^{ 0 }$
- $45^{ 0 }$
- $90^{ 0 }$
- $30^{ 0 }$
The value of $cos^2 10^o 15^o + cos^2 20^o +...... + cos^2 365^O$
- 34
- 36
- 35
- 37/2
$16 \cos^6 10^o - 24 \cos^4 10^o + 9 \cos^2 10^o$ is equal to
- $\dfrac{1}{4}$
- $\dfrac{3}{4}$
- $\dfrac{1}{2}$
- $1$
If $(1+\tan 1^{o})(1+\tan 2^{o})(1+\tan 3^{o})....(1+\tan 45^{o})=2^{n}$, then $n$ is equal to
- $21$
- $24$
- $23$
- $22$
Values of : $sin{ 10 }^{ 0 }sin{ 50 }^{ 0 }sin{ 60 }^{ 0 }sin{ 70 }^{ 0 }$ is
- $\cfrac { 3 }{ 16 } $
- $\cfrac { 5 }{ 16 } $
- $\cfrac { \sqrt { 3 } }{ 16 } $
- $\cfrac { \sqrt { 5 } }{ 16 } $
$sin^21^0+sin^22^0+sin^23^0+....+sin^290^0$
- 0
- 1
- 89/2
- 91/2
$\frac { cos{ 70 }^{ \circ } }{ sin{ 20 }^{ \circ } } +\frac { cos{ 59 }^{ \circ } }{ sin{ 31 }^{ \circ } } -8{ sin }^{ 2 }{ 30 }^{ \circ }$
- $1$
- $-1$
- $0$
- $2$
The value of $(4 , cos^2 9^o - 1) (4 cos^2 27^o - 1) (4 , cos^2 81^o - 1) (4 , cos^2 243^o - 1) $ is
- 1
- -1
- 2
- none of these
$sin{ 40 }^{ \circ }{ 35 }^{ | }cos{ 19 }^{ \circ }{ 25 }^{ | }+cos{ 40 }^{ \circ }{ 35 }^{ | }sin{ 19 }^{ \circ }{ 25 }^{ |= }$
- 1
- $\frac { \sqrt { 3 } }{ 2 } $
- $0$
- $-1$
$\sqrt {3}\csc 20^{o}-\sec 20^{o}$ is equal to
- $2$
- $2\sin 20^{o}\csc 40^{o}$
- $4$
- $4\sin 20^{o}\csc 40^{o}$.
$tan{ 40 }^{ \circ }+tan{ 80 }^{ \circ }-\sqrt { 3 } tan{ 40 }^{ \circ }tan{ 80 }^{ \circ }=$
- $\sqrt { 3 } $
- $\sqrt { -3 } $
- $\frac { 1 }{ \sqrt { 3 } }$
- $\frac { -1 }{ \sqrt { 3 } }$
$\sin^{-1}\left(\sin 100\right)+\cos^{-1}\left(\cos 100\right)+\tan^{-1}\left(\tan 100\right)+\cot^{-1}\left(\cot 100\right)$ equals to
- $100-31\pi$
- $100-32\pi$
- $200-63\pi$
- $200+63\pi$
$\dfrac{tan225 cot81cot69}{cot261 + tan21} $ =
- 1
- $\dfrac{1}{\sqrt{2}}$
- $\sqrt{3}$
- $\dfrac{1}{\sqrt{3}}$
Find the value of, $\dfrac {4}{3}\cot^{2}30^{o}+\cot^{2}60^{o}-2\csc ^{2}60^{o}-\dfrac {3}{4}\tan^{2}30^{o}$
- $10/3$
- $11/3$
- $4$
- $none\ of\ these$
$ \sqrt { 3 } \ cosec 20 ^ { \circ } - \sec 20 ^ { \circ }$ is equal to :
- $2$
- $2 \sin 20 ^ { \circ } / \sin 40 ^ { \circ }$
- $4$
- $4 \sin 20 ^ { \circ } / \sin 40 ^ { \circ }$
$Tan ,25^o.Tan ,31^o + Tan ,31^o.Tan ,34^o + Tan ,34^o .Tan ,25^o =$
- $1$
- $2$
- $3$
- $4$
Let $x=\sin 1^{o}$, then the value of expression
$\dfrac {1}{\cos 0^{o}\cos 1^{o}}+\dfrac {1}{\cos 1^{o}\cos 2^{o}}+\dfrac {1}{\cos 2^{o}\cos 3^{o}}+....+\dfrac {1}{\cos 44^{o}\cos 45^{o}}=$
- $x$
- $\dfrac {1}{x}$
- $\dfrac {\sqrt {2}}{x}$
- $\dfrac {x}{\sqrt {2}}$
$\dfrac{\cos (45^0+A)-\cos(45^0-A)}{\sin(120^0+A)-\sin(120^0-A)}=?$
- $2$
- $\sqrt{2}$
- $2\sqrt{2}$
- $2/\sqrt{2}$
if $A=30$ then the value of $\cos 2A$ is
- $1$
- $0$
- $1/2$
- $\surd {3}/2$
$(1+\tan 5^{o})(1+\tan 10^{o})(1+\tan 15^{o}).....(1+\tan 45^{o})$ is equal to
- $!$
- $32$
- $2$
- $0$
$sin 12^o\sin\ 24^o\sin\ 48^o\sin\ 84^o$=
- $\cos 20^o\cos 40^o\cos 60^o\cos 80^o$
- $\sin 20^o\sin 40^o\sin 60^o\sin 80^o$
- $\dfrac{3}{15}$
- $\dfrac{5}{16}$
$\tan 5\tan 25\tan 30\tan 65 \tan 85$ is equal to
- $3$
- $\surd {3}$
- $1$
- $\dfrac {1}{\surd {3}}$
$\tan 20 ^ { \circ } + \tan 40 ^ { \circ } + \sqrt { 3 } \tan 20 ^ { \circ } \tan 40 ^ { \circ }$ is equal to
- $\dfrac { \sqrt { 3 } } { 2 }$
- $\dfrac { \sqrt { 3 } } { 4 }$
- $\sqrt { 3 }$
- $1$
If $\alpha =685^o$, then $(\cos\alpha -\sin\alpha)$ is equivalent to?
- $-\cos 35^o-\sin 35^o$
- $-\cos 35^o +\sin 35^o$
- $\cos 35^o-\sin 35^o$
- $\cos 35^o+\sin 35^o$
The distance between $A ( \cos \theta , \sin \theta )$ and $B ( - \sin \theta , \cos \theta )$ is
- 1
- $2 + 2 \sin \theta$
- $1 + \sin \theta$
- $\sqrt { 2 }$
$\dfrac { 1 tan^{ 1 } 45^{ 2 }}{ 1 tan^{ 1 } 45^{ 0 } }$
- $tan 90^{ 0 }$
- $sin 45^{ 0 }$
- $sin 90^{ 0 }$
- $cos 90^{ 0 }$
$\displaystyle3\tan^2{30^\circ}+\frac{4}{3}\cos^2{30^\circ}-2\sin^2{45^\circ}-\frac{1}{3}\sin^2{60^\circ}$ is equal to__________________.
- $\displaystyle\frac{1}{4}$
- $\displaystyle\frac{3}{4}$
- $1$
- $0$
The angle measuring $\displaystyle \frac{\pi ^{c}}{4}$ when expressed in centesimal system is ___
- $\displaystyle 50^{g}$
- $\displaystyle 60^{g}$
- $\displaystyle 75^{g}$
- $\displaystyle 100^{g}$
$\displaystyle 30^{\circ}$ in centesimal measure is _____
- $\displaystyle \frac{50^{g}}{3}$
- $\displaystyle \frac{100^{g}}{3}$
- $\displaystyle \frac{160^{g}}{3}$
- $\displaystyle \frac{200^{g}}{3}$
When the sun is $30^o$ above the horizon, what is the length of the shadow cast by a building $40$ m high?
- $50.23$ m
- $70.24$ m
- $68.25$ m
- $69.28$ m
From the tower $30$ m above the sea, the angle of depression of a boat is $68^o$. How far is the boat from the tower?
- $12.12$ m
- $11.11$ m
- $10.10$ m
- $9.99$ m
When the sun is $50^o$ above the horizon, how long is the shadow cast by a building $16$ m high?
- $23$ m
- $13.42$ m
- $43.42$ m
- $23.42$ m