CBSE Questions for Class 10 Maths Introduction To Trigonometry Quiz 4 - MCQExams.com

The value of $$\sin^2 60^0 + \tan 45^0 - \text{cosec}^2 45^0$$ is
  • $$-\dfrac{1}{2}$$
  • $$-\dfrac{1}{4}$$
  • $$\dfrac{1}{4}$$
  • $$\dfrac{1}{2}$$
$$\dfrac{tan \theta}{(1+tan^{2} \theta)^2}+\dfrac{cot \theta}{(1+cot^{2} \theta)^2}$$ is equal to
  • $$ 2 sin \theta. cos \theta$$
  • $$ cosec \theta. sec \theta$$
  • $$ sin \theta. cos \theta$$
  • $$2 cosec \theta. sin \theta$$
Let $$x = (1 + \sin {A})(1 + \sin {B})(1 + \sin {C}), y = (1 - \sin {A})(1 - \sin {B})(1 - \sin {C})$$ and If $$x = y$$ then
  • $$x = \cos {A} \cos {B} \cos {C}$$
  • $$y = \sin {A} \sin {B} \sin {C}$$
  • $$y = -\cos {A} \cos {B} \cos {C}$$
  • $$x = - \sin {A} \sin {B} \sin {C}$$
If $$a \cos\theta-b \sin\theta=c$$, then $$a \sin\theta+b\cos\theta$$ equals-
  • $$a^2+b^2+c^2$$
  • $$a^2-b^2-c^2$$
  • $$\sqrt {a^2+b^2+c^2}$$
  • $$\pm \sqrt {a^2+b^2-c^2}$$
If $$\displaystyle \frac { \sin ^{ 4 }{ x }  }{ 2 } +\frac { \cos ^{ 4 }{ x }  }{ 3 } =\frac { 1 }{ 5 } ,$$ then:
  • $$\displaystyle \tan ^{ 2 }{ x } =\frac { 2 }{ 3 } $$
  • $$\displaystyle \frac { \sin ^{ 8 }{ x }  }{ 8 } +\frac { \cos ^{ 8 }{ x }  }{ 27 } =\frac { 1 }{ 125 } $$
  • $$\displaystyle \tan ^{ 2 }{ x } =\frac { 1 }{ 3 } $$
  • $$\displaystyle \frac { \sin ^{ 8 }{ x }  }{ 8 } +\frac { \cos ^{ 8 }{ x }  }{ 27 } =\frac { 2 }{ 125 } $$
If $$\displaystyle x=r\sin \theta \cdot \cos \phi,$$  $$y=r\sin \theta \cdot \sin \phi$$ and $$\displaystyle z= r\cos \theta$$, then the value of $$\displaystyle x^{2}+y^{2}+z^{2}$$ is independent of: 
  • $$\displaystyle \theta ,\phi$$
  • $$\displaystyle r,\theta$$
  • $$\displaystyle r,\phi$$
  • $$r$$
If $$\sin { A } =a\cos { B } $$ and $$\cos { A } =b\sin { B } $$, then $$\left( { a }^{ 2 }-1 \right) \tan ^{ 2 }{ A } +\left( 1-{ b }^{ 2 } \right) \tan ^{ 2 }{ B } $$   is equal to
  • $$\displaystyle \frac { { a }^{ 2 }-{ b }^{ 2 } }{ { b }^{ 2 } } $$
  • $$\displaystyle \frac { { a }^{ 2 }-{ b }^{ 2 } }{ { a }^{ 2 } } $$
  • $$\displaystyle \frac { { a }^{ 2 }+{ b }^{ 2 } }{ { b }^{ 2 } } $$
  • $$\displaystyle \frac { { a }^{ 2 }+{ b }^{ 2 } }{ { a }^{ 2 } } $$
If $$\displaystyle  \sin\theta + cosec \theta= 2,$$  then the value of $$\displaystyle \sin ^{8}\theta + cosec ^{8}\theta$$ is equal to
  • $$2$$
  • $$\displaystyle 2^{8}$$
  • $$\displaystyle 2^{4}$$
  • none of these
If $$\tan A+\cot A=4$$, then $$\tan^2A+\cot^2A$$ is equal to
  • $$10$$
  • $$11$$
  • $$12$$
  • $$14$$
If $$\sin A, \cos A$$ and $$\tan A$$ are in $$G.P.,$$ then $$\cot^6 A- \cot^2A$$ is equal to
  • $$-1$$
  • $$0$$
  • $$1$$
  • $$\cfrac {1}{2}$$
The value of $$\tan 5^{\circ}\tan 10^{\circ}\tan 15^{\circ}\cdots \tan 85^{\circ}$$ is
  • $$0$$
  • Not defined
  • $$1$$
  • $$-1$$
The expression $$\displaystyle f\left ( \theta \right )= \frac{1}{\tan \theta+\sec \theta+\cot \theta+\text{cosec} \theta}$$ is equivalent to
  • $$\displaystyle \frac{\text{cosec} \theta +\sec \theta+\text{cosec} \theta\sec \theta}{2\text{cosec} \theta\sec\theta}$$
  • $$\displaystyle \frac{\text{cosec} \theta -\sec \theta-\text{cosec} \theta\sec \theta}{2\text{cosec}\theta\sec\theta}$$
  • $$\displaystyle \frac{\text{cosec} \theta +\sec \theta-\text{cosec} \theta\sec \theta}{2\text{cosec}\theta\sec\theta}$$
  • None of these
$$ABC$$ is an isosceles right-angled triangle. Assuming $$AB= BC= x$$, find the value of each of the following trigonometric ratios:
$$\sin 45^{0}$$ is $$\displaystyle \dfrac{1}{\sqrt{m}}$$, the value of $$m$$ is 

184308.jpg
  • 1
  • 3
  • 2
  • 4
Choose the correct option for the following.
The value of $$\displaystyle \frac{\cos 3A-2\cos 4A}{\sin 3A+2\sin 4A}$$ is $$\displaystyle \frac{1-\sqrt{2}}{1+\sqrt{6}}$$, when $$A= 15^{0}$$.
  • True
  • False
  • Ambiguous
  • Data insufficient
If $$\tan \angle ADC= 1$$ and $$\sin \angle ABC=4:5$$, then measure of $$CD$$ is: 

187003_c05f539d2d244f3c89e48a8d7c71aa9d.png
  • $$10$$
  • $$20$$
  • $$30$$
  • $$40$$
Find the length of $$AB$$ in cm
187593_5777284f055742489e1e2697b2823e96.png
  • 39.25
  • 81.96
  • 46.32
  • 85.34
The length of $$AD$$ (in cm.) is
187428.png
  • $$10$$
  • $$100$$
  • $$75$$
  • $$50$$
In the given figure; $$BC= 15$$ cm  and $$\displaystyle \sin B= \frac{4}{5}$$.
The measure of $$AC$$ in cm is

186999_7bd76132660f466cb6fef0a54ce15e26.png
  • $$10$$
  • $$15$$
  • $$20$$
  • $$19$$
Find $$PQ$$, if $$\displaystyle AB = 150\ m, \angle P = 30^{\circ}$$ and $$\displaystyle \angle Q = 45^{\circ}$$
187681_4cbfe876b614462b89d6b7d01f3d0ce6.png
  • $$978.8$$
  • $$524.4$$
  • $$279.9$$
  • $$409.8$$
If in given figure $$AD= 2$$ cm, then value of $$AB$$ ( in cm )  is 
187601_352714e8102e4942922bc4252dd6c9f9.png
  • 2
  • 3
  • 7
  • 1
In the given figure, $$\displaystyle \angle B = 60^{\circ}, \angle C =30^{\circ}, AB=8\ cm$$ and $$\displaystyle BC=25\ cm$$. 
Calculate $$BE$$ in cm.

187620_b16418eb3e3a40c4862d7d01397dbc82.png
  • 4
  • 2
  • 5
  • 7
Find :
$$AD$$

187639.bmp
  • 2
  • 6
  • 4
  • 1
If $$\sin x+\sin^2x+\sin^3x=1$$, then $$\cos^6x-4\cos^4x+8 \cos^2x$$ is equal to
  • $$0$$
  • $$2$$
  • $$4$$
  • $$8$$
If $$\cos 1^o \cos 2^o \cos 3^o ... \cos {179}^o=x+1$$, then $$x$$ is equal to
  • $$-1$$
  • $$0$$
  • $$1$$
  • none of these
For all values of $$\alpha$$ the given expression is equal to:
 $$(sin\alpha+cosec \alpha)^2+(cos\alpha+sec\alpha)^2-(tan^2\alpha+cot^2\alpha)$$ 
  • $$0$$
  • $$2$$
  • $$4$$
  • $$7$$
If $$0 < A < \pi /2$$ the value of the expression $$\dfrac {tan A}{1-cot A}+\dfrac {cot A}{1-tan A}-sec A cosec A$$ is equal to
  • -1
  • 0
  • 1
  • sin A + cos A
If $$\displaystyle \tan A=1 $$ and $$\displaystyle \tan B=\sqrt{3}$$ evaluate:$$\displaystyle \cos A\cos B-\sin A\sin B$$
  • $$\displaystyle \frac{\sqrt{2}+\sqrt{6}}{4}$$
  • $$\displaystyle \frac{\sqrt{2}-\sqrt{6}}{6}$$
  • $$\displaystyle \frac{1-\sqrt{3}}{2\sqrt2}$$
  • $$\displaystyle \frac{\sqrt{2}+\sqrt{6}}{6}$$
If $$cos x+sin x=\sqrt 2 cos x$$, then $$tan^2x+2 tan x$$ is equal to
  • $$0$$
  • $$1$$
  • $$2$$
  • $$3$$
If $$\sec C$$ is $$\displaystyle \frac{m}{2\sqrt{2}}$$, then $$m$$ is: 
196004.png
  • 1
  • 3
  • 7
  • 5
In the following figure, cosec A is $$\displaystyle \frac{5}{m}$$, m is 
196004.png
  • $$1$$
  • $$4$$
  • $$3$$
  • $$2$$
0:0:1


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