CBSE Questions for Class 11 Engineering Maths Trigonometric Functions Quiz 1 - MCQExams.com

The number of $$x\epsilon [0, 2\pi]$$ for which $$|\sqrt {2\sin^{4} x + 18\cos^{2}x} - \sqrt {2\cos^{4} x + 18\sin^{2} x}| = 1$$ is:
  • $$4$$
  • $$2$$
  • $$6$$
  • $$8$$
For $$x  \in (0, \pi)$$, the equation $$\sin x + 2 \sin 2 x - \sin 3x =3$$, has 
  • infinitely many solutions
  • three solutions
  • one solution
  • no solution
If $$0^{\circ}\leq \theta\leq 90^{\circ}$$ and $$\sqrt{3} tan\theta - sec\theta=1$$, then $$\theta$$ has the value
  • $$30^{\circ}$$
  • $$45^{\circ}$$
  • $$60^{\circ}$$
  • $$90^{\circ}$$
The of value of $$\quad \sin60^{\small\circ}\cos30^{\small\circ} + \cos60^{\small\circ}\sin30^{\small\circ}$$ is equal to
  • $$\sin 90^0$$
  • $$\sin 45^0$$
  • $$\sin 180^0$$
  • $$\sin 30^0$$
Which one of the following relations is true ?
  • $$\cos^2 \theta - \sin^2 \theta=1$$
  • $$\text{cosec}^2 \theta - \sec^2 \theta=1$$
  • $$\cot^2 \theta - \tan^2 \theta=1$$
  • $$\sec^2 \theta - \tan^2 \theta=1$$
Which is true for all values of $$\theta$$?
  • $$\sin^2 \theta -\cos^2\theta=1$$
  • $$\text{cosec}^2\theta- \cot^2 \theta=1$$
  • $$\text{cosec}^2 \theta - \cos^2 \theta=1$$
  • $$\sec^2 \theta - \sin^2 \theta=1$$
If $$0^{\circ} \leq \theta \leq 90^{\circ}$$ and $$\sqrt{2} tan \theta - sec \theta =0$$, then the value of $$(\sqrt{2} sin  \theta + 2 tan  \theta)$$ is -
  • $$\sqrt{2}+2$$
  • $$\frac{\sqrt{2}}{2} + \frac{2}{\sqrt{3}}$$
  • 3
  • 2
The value of $$ 1+ \cot^2 A$$ is
  • $$\cos^2 A$$
  • $$\sec^2 A$$
  • $$\tan^2 A$$
  • $$\text{cosec}^2 A$$
$$sin^2x+cos^2x=$$
  • 0
  • $$\sqrt{2}$$
  • 1
  • -1
The solution of equation $$\cos^2 \theta +\sin \theta+1=0$$ lies in the interval
  • $$\displaystyle \left ( - \frac{\pi}{4}, \frac{\pi}{4} \right )$$
  • $$\displaystyle \left ( \frac{\pi}{4}, \frac{3\pi}{4} \right )$$
  • $$\displaystyle \left ( \frac{3\pi}{4}, \frac{5\pi}{4} \right )$$
  • $$\displaystyle \left ( \frac{5\pi}{4}, \frac{7\pi}{4} \right )$$
The value of $$5\tan ^{ 2 }{ \theta  } -5\sec ^{ 2 }{ \theta  } $$ is :
  • $$1$$
  • $$-5$$
  • $$0$$
  • $$5$$
$$\displaystyle \frac { \sin { A }  }{ 1+\cos { A }  } +\frac { \sin { A }  }{ 1-\cos { A }  } $$ is equal to :
  • $$\displaystyle \sin { A } $$
  • $$\displaystyle 2cosecA$$
  • $$\displaystyle \cos { A } $$
  • None of these
The minimum value of $$ \displaystyle  \sec ^{2}\alpha + \cos ^{2}\alpha   $$ is 
  • $$1$$
  • $$2$$
  • $$0$$
  • $$-1$$
$$\cfrac { \tan { \theta  }  }{ \sec { \theta  } -1 } +\cfrac { \tan { \theta  }  }{ \sec { \theta  } +1 } $$ is equal to
  • $$\text{cosec} { \theta } $$
  • $$2\text{cosec} { \theta } $$
  • $$\sec { \theta } $$
  • $$2\sec { \theta } $$
If $$\sin { \theta  } +\cos { \theta  } =p$$ and $$\tan { \theta  } +\cot { \theta  } =q$$, then $$q\left( { p }^{ 2 }-1 \right) =$$
  • $$\dfrac { 1 }{ 2 } $$
  • $$2$$
  • $$1$$
  • $$3$$
$$\cfrac { 1 }{ \sec { \theta  } -\tan { \theta  }  } $$ is equal to
  • $$\sec { \theta } -\tan { \theta } $$
  • $$\sec { \theta } \tan { \theta } $$
  • $$\sec { \theta } +\tan { \theta } $$
  • $$\sec { \theta } $$
If $$\tan\theta +\cot\theta =2$$, then the value of $$\tan^2\theta +\cot^2\theta$$ is __________?
  • $$4$$
  • $$2$$
  • $$\displaystyle\frac{3}{2}$$
  • $$5$$
$$\cos ^{ 4 }{ A } -\sin ^{ 4 }{ A } $$ is equal to
  • $$\sin { 2A } $$
  • $$-\sin { 2A } $$
  • $$\cos { 2A } $$
  • $$-\cos { 2A } $$
What is $$\tan ( 360^o - A)$$?
  • $$\tan A$$
  • $$-\tan A$$
  • $$\cot A$$
  • $$-\cot A$$
Value of $$\theta (0 < \theta < 360^o )$$ which satisfy the equation $$ \text{cosec }\theta +2 =0$$ is:
  • $$210^o, 100^o$$
  • $$240^o, 300^o$$
  • $$210^o, 240^o$$
  • $$210^o, 330^o$$
If $${\tan ^2}\theta  = 2\,{\tan ^2}\phi  + 1$$, then the value of $$\cos \,2\theta  + {\sin ^2}\phi \,is$$ is
  • $$1$$
  • $$2$$
  • $$-1$$
  • $$0$$
If $$(1 - \cos A)/2 = x$$, then the value of $$x$$ is
  • $$co{s^2}(A/2)$$
  • $$\sqrt {\sin (A/2)} $$
  • $$\sqrt {\cos (A/2)} $$
  • $${\sin ^2}(A/2)$$
The solution set of the equation $$4\sin \theta \cos \theta  - 2\cos \theta  - 2\sqrt 3 \sin \theta  + \sqrt 3  = 0$$ in the interval $$(0,2\pi )$$ is-
  • $$\left\{ {\frac{{3\pi }}{4},\frac{{7\pi }}{4}} \right\}$$
  • $$\left\{ {\frac{\pi }{3},\frac{{5\pi }}{3}} \right\}$$
  • $$\left\{ {\frac{\pi }{3},\frac{{5\pi }}{3},\frac{{3\pi }}{4},\frac{{7\pi }}{4}} \right\}$$
  • $$\left\{ {\frac{\pi }{6},\frac{{5\pi }}{6},\frac{{11\pi }}{6}} \right\}$$
The solution of 
$$\frac{{3\sin \theta  - \sin 3\theta }}{{1 + \cos \theta }} + \frac{{3\cos \theta  + \cos 3\theta }}{{1 - \sin \theta }} = 4\sqrt 2 \cos \left( {\theta  + \frac{\pi }{4}} \right)$$
  • $$n\pi $$
  • $$n\pi + \frac{\pi }{{12}}$$
  • $$n\pi \pm \frac{\pi }{2}$$
  • $$2n\pi $$
A minimum value of $$\sin{x}\cos{2x}$$ is-
  • $$1$$
  • $$-1$$
  • $$-2/3\sqrt{6}$$
  • None of these
If $$\tan\theta +\tan 4\theta +\tan 7\theta =\tan \theta \tan 4\theta \tan 7\theta$$, then the general solution is?
  • $$\theta =\dfrac{n\pi}{4}$$
  • $$\theta =\dfrac{n\pi}{12}$$
  • $$\theta =\dfrac{n\pi}{6}$$
  • None of these
If $$\cot\left( {a + \beta } \right) = 0,$$ then $$\sin\left( {a + 2\beta } \right)$$ can be 
  • $$-\sin a$$
  • $$\sin \beta $$
  • $$\cos a$$
  • $$\cos \beta $$
The solutions of the equation $$\sin x+3\sin 2x+\sin 3x=\cos x+3\cos 2x+\cos 3x$$ in the interval $$0\le x\le 2\pi$$, are 
  • $$\dfrac{\pi}{8}, \dfrac{5\pi}{8}, \dfrac{2\pi}{3}$$
  • $$\dfrac{\pi}{8}, \dfrac{5\pi}{8}, \dfrac{9\pi}{8}, \dfrac{13\pi}{8}$$
  • $$\dfrac{4\pi}{3}, \dfrac{9\pi}{3}, \dfrac{2\pi}{3}, \dfrac{13\pi}{8}$$
  • $$\dfrac{\pi}{8}, \dfrac{5\pi}{8}, \dfrac{9\pi}{3}, \dfrac{4\pi}{3}$$
If $$ X\sin { \left( { 90 }^{ \circ  }-\theta  \right) \cot { \left( { 90 }^{ \circ  }-\theta  \right)  }  } =\cos { \left( { 9 }0^{ \circ  }-\theta  \right)  } $$, then x =
  • 0
  • 1
  • -1
  • 2
Select write the most appropriate answer from the given alternative in each following questions:-
The principal solution of tan $$x=-\sqrt{3}$$ are: 
  • $$\frac{-\pi }{3}and \frac{2\pi }{3}$$
  • $$\frac{\pi }{3}and \frac{5\pi }{3}$$
  • $$\frac{2\pi }{3}and \frac{5\pi }{3}$$
  • $$\frac{2\pi }{3}and \frac{4\pi }{3}$$
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