CBSE Questions for Class 10 Maths Introduction To Trigonometry Quiz 13 - MCQExams.com

If $$\cot\theta+\tan\theta=x$$ and $$\sec\theta-\cos\theta=y$$, then
  • $$\sin\theta \cos\theta=\displaystyle \cfrac {1}{x}$$
  • $$\sin\theta \tan\theta=y$$
  • $$(x^2y)^{2/3}=1$$
  • $$(x^2y)^{1/3}+(xy^2)^{1/3}=1$$
If $$x=\dfrac {\sin^3p}{\cos^2p}, y=\dfrac {\cos^3p}{\sin^2p}$$ and $$\sin p + \cos p= \dfrac 12$$, then $$x+y$$ is equal to
  • $$\cfrac {75}{18}$$
  • $$\cfrac {44}{9}$$
  • $$\cfrac {79}{18}$$
  • $$\cfrac {48}{9}$$
In the figure given
$$\angle ABD=\angle PQD=\angle CDQ=\cfrac { \pi  }{ 2 } $$. If $$AB=x.PQ=z$$ and $$CD=y$$, then which one of the following is correct?
551936.PNG
  • $$\cfrac { 1 }{ x } +\cfrac { 1 }{ y } =\cfrac { 1 }{ z } $$
  • $$\cfrac { 1 }{ x } +\cfrac { 1 }{ z } =\cfrac { 1 }{ y } $$
  • $$\cfrac { 1 }{ z } +\cfrac { 1 }{ y } =\cfrac { 1 }{ x } $$
  • $$\cfrac { 1 }{ x } +\cfrac { 1 }{ y } =\cfrac { 2 }{ z } $$
Find the relation obtained by eliminating $$\displaystyle \theta $$ from the equation $$\displaystyle x=a\cos \theta +b\sin \theta  $$ and $$\displaystyle y=a\sin \theta -b\cos \theta $$
  • $$\displaystyle x^{2}+y^{2}=a^{2}-b^{2}$$
  • $$\displaystyle x^{2}-y^{2}=a^{2}+b^{2}$$
  • $$\displaystyle x^{2}-y^{2}=a^{2}-b^{2}$$
  • $$\displaystyle x^{2}+y^{2}=a^{2}+b^{2}$$
Which one of the following when simplified is not equal to one?
  • $$\displaystyle \tan 18^{\circ}\times \tan 36^{\circ}\times \tan 54^{\circ}\times \tan 72^{\circ}$$
  • $$\displaystyle \sin ^{2}19^{\circ}+\sin ^{2}71^{\circ}$$
  • $$\displaystyle \frac{2\sin 62^{\circ}}{\cos 28^{\circ}}-\frac{\sec 42^{\circ}}{\text{cosec}48^{\circ}}$$
  • None of these
If $$\frac{1 - cos x}{cos x (1 + cos x)} = \frac{sin \alpha}{cos x} - \frac{2}{1 + cos x}$$, then $$\alpha$$ =
  • $$\frac{\pi}{8}$$
  • $$\frac{\pi}{4}$$
  • Both A and B
  • None of the above
$$\dfrac { cot\theta +cosec\theta -1 }{ cot\theta -cosec\theta +1 } $$ is equal to:
  • $$\dfrac { 1+cos\theta }{ sin\theta } $$
  • $$\dfrac { sin\theta }{ 1+cos\theta } $$
  • $$\dfrac { sin\theta }{ 1-cos\theta } $$
  • $$\dfrac { 1-cos\theta }{ sin\theta } $$
If $$\cos P=\dfrac{1}{7}$$ and $$\cos Q=\dfrac{13}{14}$$, P and Q both are acute angle then the value of $$P-Q$$ will be?
  • $$45^o$$
  • $$30^o$$
  • $$75^o$$
  • $$60^o$$
$$\sin { { 48 }^{ 0 } } .\sin { 12^{ 0 } } =$$
  • $$\frac { 1+\sqrt { 5 } }{ 8 } $$
  • $$\frac { 1-\sqrt { 5 } }{ 8 } $$
  • $$\frac { \sqrt { 5 } +1 }{ 8 } $$
  • $$\frac { \sqrt { 5 } -1 }{ 8 } $$
$$1+cosec\dfrac { \pi }{ 4 } +cosec\dfrac { \pi }{ 8 } +cosec\dfrac { \pi }{ 16 } =$$
  • $$cot\dfrac { \pi }{ 8 } $$
  • $$cot\dfrac { \pi }{ 16 } $$
  • $$cot\dfrac { \pi }{ 32 } $$
  • $$cosec^{ 2 }\dfrac { \pi }{ 16 } $$
$$\frac { \sec { 8A } -1 }{ \sec { 4A } -1 } =$$
  • $$0$$
  • $$\frac { \tan { 8A } }{ \tan { 2A } } $$
  • $$\frac { \cos { 8A } }{ \cos { 2A } } $$
  • $$\frac { \sin { 8A } }{ \sin { 2A } } $$
$$\dfrac { tan\theta  }{ 1-cot\theta  } +\dfrac { cot{\theta}}{ 1-tan\theta  } $$ is equal to:
  • $$1+sin\theta cost\theta $$
  • $$sin\theta cos\theta $$
  • $$sec\theta cosec\theta $$
  • $$1+sec\theta cosec\theta $$
Suppose $$I_1 = \displaystyle \int_0^{\pi/2} cos(\pi sin^2x)dx; I_2 =  \displaystyle \int_0^{\pi/2} cos(2\pi sin^2x)dx \,and \, I_3 =  \displaystyle \int_0^{\pi/2} cos(\pi sin x)dx$$ then
  • $$I_1 = 0$$
  • $$I_2 + I_1 = 0$$
  • $$I_1 + I_2 + I_3 = 0$$
  • $$I_2 = I_3$$
$$1+cosec\frac { \pi  }{ 4 } +cosec\frac { \pi  }{ 8 } cosec\frac { \pi  }{ 16 } =$$
  • $$cot\frac { \pi }{ 8 } $$
  • $$cot\frac { \pi }{ 16 } $$
  • $$cot\frac { \pi }{ 32 } $$
  • $${ cosec }^{ 2 }$$
If $$cos(80^{\circ}+\Theta )=sin(\frac{k}{3})-\Theta )$$ then k=.....
  • 81
  • 27
  • 54
  • 9
If the median of a triangle ABC passing through A is perpendicular AB then tanA + 2tanB = 
  • 1
  • 1
  • 0
  • None
An angle is increasing at a constant rate. The rate of increase of tan when the angle is $$ \pi /3 $$ is 
  • 4 times the increase of sine
  • 8 times the increase of cosine
  • 8 times the increase of sine
  • 4 times the increase of cosine
$$\dfrac{cos A}{1+sin A} +\dfrac{cos A}{1-sin A} =$$
  • $$ 2 sec A$$
  • $$ 2 cos A$$
  • $$2$$
  • $$0$$
The value of $$\cfrac { cot{ 54 }^{ 0 } }{ cot36^{ 0 } } +\cfrac { tan{ 20 }^{ 0 } }{ cot{ 70 }^{ 0 } } =$$.
  • 3
  • 1
  • 0
  • 2
In triangle ABC, if $$sinAcosB=\cfrac { 1 }{ 4 } $$ and $$3tanA=tanB$$ then $${ cot }^{ 2 }A$$ is equal to 
  • 2
  • 3
  • 4
  • 5
If $$\sec \theta + \tan \theta = x,$$ then $$\sec \theta = ........... .$$
  • $$\frac{x^2 + 1}{x}$$
  • $$\frac{x^2 + 1}{2x}$$
  • $$\frac{x^2 - 1}{2x}$$
  • $$\frac{x^2 - 1}{x}$$
$$\frac { cos\theta  }{ sec\theta +tan\theta  } +\frac { cos\theta  }{ sec\theta -tan\theta  } $$=
  • 1
  • $$cos\theta$$
  • $$sin\theta$$
  • 2
$$\dfrac{sin A}{cosec A} + \dfrac{cosA}{sec A}$$ =
  • $$1$$
  • $$sin^2A$$
  • $$ 2 sin^2 A+ cos ^2 A$$
  • $$ 2 sec A$$
If $$tanA=\sqrt { 2 } -1,\quad then\quad the\quad value\quad of\quad cosec.\quad A.secA\quad is\quad equal\quad to\quad $$ 
  • $$\dfrac { 1 }{ \sqrt { 2 } } $$
  • $$\dfrac { 1 }{ \sqrt { 2 } } $$
  • $$2\sqrt { 2 } $$
  • $$\dfrac { \sqrt { 3 } }{ 2 } $$
$$tan^{-1} \begin {pmatrix} \cfrac {1+sinx}{cos x}\end {pmatrix}=$$
  • $$\cfrac {\pi}4- \cfrac {x}2$$
  • $$\cfrac {\pi}4- {x}$$
  • $$\cfrac {\pi}4+ {x}$$
  • $$\cfrac {\pi}4+\cfrac {x}2$$
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 10 Maths Quiz Questions and Answers