CBSE Questions for Class 11 Engineering Maths Trigonometric Functions Quiz 12 - MCQExams.com

$$\cos^ {2}\theta \left(1+\tan^ {2}\theta\right)=1$$
  • True
  • False
 $$\csc^{6}\theta -\cot^{6}\theta =1+3\csc^{2}\theta \cot^{2}\theta$$ 
  • True
  • False
If $$x=a\cos\theta+b\sin\theta$$ and $$y=a\sin\theta-b\cos\theta$$, then $$a^{2}+b^{2}=x^{2}+y^{2}$$.
  • True
  • False
$$(\cos A-\csc A)^{2}+(\sin A-\sec A)^{2}=(1-\sec A.\csc A)^{2}$$
  • True
  • False
If $$\sin \theta  +\sin^{2}\theta +\sin^{3}\theta =1$$, then $$ \cos^{6}\theta -4\cos^{4}\theta +8 \cos^{2}\theta =4$$.
  • True
  • False
$$\sqrt{\dfrac{\sec A-1}{\sec A+1}}+\sqrt{\dfrac{\sec A+1}{\sec A-1}}=2\csc A$$
  • True
  • False
State true or false.
$$ \dfrac{\tan^{2}\theta }{\sec^{2}\theta}+\dfrac{\cot^{2}\theta }{cosec^{2}\theta}=1 $$
  • True
  • False
State whether the following statement is true or false.
$$\dfrac { \sin A }{ \sec A+\tan A-1 } +\dfrac { \cos A }{ \text{cosec}A+\cot A-1 } =1$$
  • True
  • False
$$\left( \csc { A-\sin { A }  }  \right) \left( \sec { A-\cos { A }  }  \right) =\dfrac { 1 }{ \tan { A+\cot { A }  }  }$$ 
  • True
  • False
Check whether following statement is true or false.
$${ \cos }^{ 4 } \theta -{ \sin }^{ 4 }\theta = 1+2{ \sin }^{ 2 } \theta $$
  • True
  • False
State whether the following statement is true or false.
$$\dfrac { 1 }{ \sec { A } +\tan { A }  } -\dfrac { 1 }{ \cos { A }  } =\dfrac { 1 }{ \cos { A }  } -\dfrac { 1 }{ \sec { A } -\tan { A }  } $$
  • True
  • False
$$\dfrac{\cos\theta-\sin \theta+1}{\cos\theta+\sin \theta-1}=\text{cosec} \theta+\cot \theta$$
  • True
  • False
State whether the following statement is true or false.
$$\dfrac { \cos A-\sin A+1 }{ \cos A+\sin A-1 }= \text{cosec} A+\cot A$$. (by using the identity $$ \text{cosec}^{ 2 }A=1+{ \cot }^{ 2 }A.)\quad $$
  • True
  • False
The value of $$\dfrac{\cos^{2}\theta+\tan^{2}\theta\ -1}{\sin^{2}\theta}$$ is
  • $$0$$
  • $$\cos^{2}\theta$$
  • $$\tan^{2}\theta$$
  • $$\dfrac{1}{\sin^{2}\theta}$$
State whether the following statement is true or false.
$$\dfrac { \cot A-\cos A }{ \cot A+\cos A } =\dfrac { \text{cosec}A-1 }{ \text{cosec}A+1 } $$
  • True
  • False
State whether the following statement is true or false.
$$\dfrac{1}{secA-1}+\dfrac{1}{secA+1}=2cosecAcotA$$
  • True
  • False
State whether the following statement is true or false.
$$\sec { ^{ 4 } } A\left( 1-\sec { ^{ 4 } } A \right) -2\tan { ^{ 2 } } A=1$$
  • True
  • False
State whether the following statement is true or false.
If $$\cos A+{ \cos }^{ 2 }A=1,$$ then $${ \sin }^{ 2 }A+{ \sin }^{ 4 }A=1.$$
  • True
  • False
If $${ cosec }\theta -cot\theta =p$$, then $$cosec\theta +cot\theta =$$

  • 1/p
  • -1/p
  • -p
  • $${ p }^{ 2 }$$
State whether the following statement is true or false.
$$\dfrac { 1+\cos\theta -\sin^{ 2 }\theta  }{ \sin { \theta \left( 1+\cos { \theta  }  \right)  }  } =\cot { \theta  }$$
  • True
  • False
$$\dfrac{{\tan\theta }}{{1 - \cot \theta }} + \dfrac{{\cot \theta }}{{1 - \tan \theta }} = 1 + \sec \theta .\text{cosec}\theta $$
  • True
  • False
The value of $$\sin \theta$$ is not equal to
  • $$\pm \frac{1}{2}$$
  • $$\frac{1}{\sqrt 2}$$
  • $$\pm \frac{1}{3}$$
  • $$2$$
The maximum value of $$2 \sin x-4 \cos x$$ is
  • $$-\sqrt { 12 } $$
  • $$2$$
  • $$\sqrt { 20 } $$
  • None of these
The value of $$\sin\theta$$ is not equal to
  • $$\pm\dfrac {1}{2}$$
  • $$\dfrac {1}{\sqrt {2}}$$
  • $$\pm\dfrac {1}{3}$$
  • $$2$$
If $$x_{1}$$ and $$x_{2}$$ are two distinct roots of the equation $$a\cos x+b\sin x=c$$, then $$\tan\dfrac {x_{1}+x_{2}}{2}$$ is equal to
  • $$a/b$$
  • $$b/a$$
  • $$c/a$$
  • $$a/c$$
$$\dfrac{1-\sin A}{1+\sin A}=(\sec A -\tan A)^2$$
  • True
  • False
If $$sin{(2cos^{-1}(\dfrac{1}{\sqrt{5}})} + cos{(2tan^{-1}(\dfrac{1}{3}))}=\dfrac{p}{q}$$, where p & q are relatively prime then digit at units place of $${(p-q)}^{2k+1}, k\epsilon{N}$$, can be ________.
  • 1
  • 3
  • 7
  • 9
Given $$A={ sin }^{ 2 }\theta +{ cos }^{ 4 }\theta $$, then for all real $$\theta $$
  • $$1\le A\le 2$$
  • $$\cfrac { 3 }{ 4 } \le A\le 1$$
  • $$\cfrac { 13 }{ 16 } \le A\le 1$$
  • $$\cfrac { 3 }{ 4 } \le A\le \cfrac { 13 }{ 16 } $$
The values of x in $$\left(0, \dfrac{\pi}{2}\right)$$ satisfying the equation $$\sin x\cos x=\dfrac{1}{4}$$ are ________.
  • $$\dfrac{\pi}{6}, \dfrac{\pi}{12}$$
  • $$\dfrac{\pi}{12}, \dfrac{5\pi}{12}$$
  • $$\dfrac{\pi}{8}, \dfrac{3\pi}{8}$$
  • $$\dfrac{\pi}{8}, \dfrac{\pi}{4}$$
What is $$\cot(\dfrac{A}{2})-\tan(\dfrac{A}{2})$$ equal to ?
  • $$\tan A$$
  • $$\cot A$$
  • $$2\tan A$$
  • $$2\cot A$$
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