CBSE Questions for Class 11 Engineering Maths Trigonometric Functions Quiz 6 - MCQExams.com

The least positive root of the equation $$\cos 3x+\sin 5x=0$$ is,
  • $$\dfrac{3 \pi}{16}$$
  • $$\dfrac{ \pi}{16}$$
  • $$\dfrac{7 \pi}{16}$$
  • $$\dfrac{9 \pi}{16}$$
The value of $$\displaystyle \cos { \frac { \pi  }{ 15 }  } \cos { \frac { 2\pi  }{ 15 }  } \cos { \frac { 4\pi  }{ 15 }  } \cos { \frac { 8\pi  }{ 15 }  } $$ is
  • $$\displaystyle \frac { 1 }{ 16 } $$
  • $$\displaystyle -\frac { 1 }{ 16 } $$
  • $$\displaystyle 1$$
  • $$\displaystyle 0$$
If $$f(x)=\cos ^{ 2 }{ x } +\cos ^{ 2 }{ 2x } +\cos ^{ 2 }{ 3x } $$, then the number of values of $$x\in \left[ 0,2\pi  \right] $$ for which $$f(x) = 0$$ are
  • $$4$$
  • $$6$$
  • $$8$$
  • $$0$$
If $$\sin x = \dfrac {1}{2}$$ and $$\cos x < 0$$, then $$x =$$
  • $$-\dfrac {\pi}{6}$$
  • $$\dfrac {\pi}{6}$$
  • $$\dfrac {\pi}{2}$$
  • $$\dfrac {2\pi}{3}$$
  • $$\dfrac {5\pi}{6}$$
Find the positive value of $$sin (tan^{-1} 3)$$
  • $$\dfrac{3}{10}$$
  • $$\dfrac{3}{5}$$
  • $$\dfrac{3}{\sqrt{10}}$$
  • $$\dfrac{1}{3}$$
  • $$\dfrac{1}{\sqrt{10}}$$
$$2 \cos^3 A \,\sin\, A + 2\, \sin^3 A\, \cos\, A$$ equals which one of the following?
  • $$\cos 2A$$
  • $$2 \sin A$$
  • $$2 \cos A$$
  • $$\cos^2 A$$
  • $$\sin 2A$$
For acute angle $$\theta$$, find $$\text{cosec }^{2}\theta - \cot^{2}\theta$$
  • $$2$$
  • $$3$$
  • $$0$$
  • $$1$$
For acute angle $$\theta$$, find value of $$\sec^{2}\theta - \tan^{2} \theta$$
  • $$1$$
  • $$2$$
  • $$3$$
  • $$0$$
In any right angled triangle which of the following identity is true?
  • $$\sin^{2}\theta - \cos^{2}\theta = 1$$
  • $$\cos^{2}\theta = 1 + \sin^{2} \theta$$
  • $$1 + \tan^{2}\theta = \sec^{2}\theta$$
  • $$\sec^{2}\theta + 1 = \tan^{2}\theta$$
$$(\cos^{2} \theta - 1)(\cot^{2}\theta + 1) + 1 =$$
  • $$1$$
  • $$-1$$
  • $$2$$
  • $$0$$
The value of $$\left( 1+\tan ^{ 2 }{ \theta  }  \right) \sin ^{ 2 }{ \theta  } $$ is
  • $$\sin ^{ 2 }{ \theta }$$
  • $$\cos ^{ 2 }{ \theta }$$
  • $$\tan ^{ 2 }{ \theta }$$
  • $$\cot ^{ 2 }{ \theta }$$
The value of $$9\tan ^{ 2 }{ \theta  } -9\sec ^{ 2 }{ \theta  } $$ is
  • $$1$$
  • $$0$$
  • $$9$$
  • $$-9$$
$$(1 + tan^2 \theta) . sin^2 \theta = $$
  • $$sin^2 \theta$$
  • $$cos^2 \theta$$
  • $$tan^2 \theta$$
  • $$cot^2 \theta$$
If $$x = a \sec \theta, y = b\tan \theta$$, then the value of $$\dfrac {x^{2}}{a^{2}} - \dfrac {y^{2}}{b^{2}} =$$
  • $$1$$
  • $$-1$$
  • $$\tan^{2}\theta$$
  • $$cosec^{2}\theta$$
If $$\sin( \pi \cos \theta) = \cos (\pi \sin \theta)$$, then which of the following is correct.
  • $$\cos \theta =\dfrac {3}{2\sqrt {2}}$$
  • $$\cos \left (\theta - \dfrac {\pi}{2}\right ) = \dfrac {1}{2\sqrt {2}}$$
  • $$\cos \left (\theta - \dfrac {\pi}{4}\right ) = \dfrac {1}{2\sqrt {2}}$$
  • $$\cos \left (\theta + \dfrac {\pi}{4}\right ) = -\dfrac {1}{2\sqrt {2}}$$
$$\displaystyle \left ( 1+\cot^{2}\theta \right )\left ( 1-\cos\theta \right )\left ( 1+\cos\theta \right )=$$
  • $$\tan^{2}\theta-\sec^{2}\theta$$
  • $$\sin^{2}\theta-\cos^{2}\theta$$
  • $$\sec^{2}\theta-\tan^{2}\theta$$
  • $$\cos^{2}\theta-\sin^{2}\theta$$
Principal solutions of the equation $$\sin { 2x } +\cos { 2x } =0$$, where $$\pi< x< 2\pi$$ are
  • $$\cfrac { 7\pi }{ 8 } ,\cfrac { 11\pi }{ 8 } $$
  • $$\cfrac {9 \pi }{ 8 } ,\cfrac { 13\pi }{ 8 } $$
  • $$\cfrac { 11\pi }{ 8 } ,\cfrac { 15\pi }{ 8 } $$
  • $$\cfrac { 15\pi }{ 8 } ,\cfrac { 19\pi }{ 8 } $$
The number of solutions $$\left[ \cos { x }  \right] +\left| \sin { x }  \right| =1$$ in $$\pi \le x < 3\pi $$, where $$[x]$$ is the greatest integer not exceeding $$x$$ is
  • $$3$$
  • $$4$$
  • $$2$$
  • $$1$$
$$9\tan^{2}\theta - 9 \sec^{2}\theta =$$
  • $$1$$
  • $$0$$
  • $$9$$
  • $$-9$$
The number of roots of the equation $$x + 2\tan x = \dfrac {\pi}{2}$$ in the interval $$[0, 2\pi]$$ is
  • $$1$$
  • $$2$$
  • $$3$$
  • Infinite
The number of principal solutions of $$\tan 2\theta = 1$$ is
  • One
  • Two
  • Three
  • Four
The equation $$ \sqrt {3} \sin x + \cos x = 4 $$ has 
  • Infinitely many solutions
  • No solution
  • Two solutions
  • Only one solution
If $$\cos { \alpha  } +\cos { \beta  } +\cos { \gamma  } =\sin { \alpha  } +\sin { \beta  } +\sin { \gamma  } =0$$, then the value of $$\cos { 3\alpha  } +\cos { 3\beta  } +\cos { 3\gamma  } $$ is
  • $$0$$
  • $$\cos { \left( \alpha +\beta +\gamma \right) } $$
  • $$3\cos { \left( \alpha +\beta +\gamma \right) } $$
  • $$3\sin { \left( \alpha +\beta +\gamma \right) } $$
If $$0\le x\le 2\pi $$, then the number of solutions of the equation $$\sin ^{ 6 }{ x } +\cos ^{ 6 }{ x } =1$$ is
  • $$2$$
  • $$3$$
  • $$4$$
  • $$5$$
  • $$8$$
Principal solutions of the equation $$\sin 2x+\cos2x=0$$, where $$\pi < x < 2\pi$$ are
  • $$7\dfrac{\pi}{8}, 11\dfrac{\pi}{8}$$
  • $$9\dfrac{\pi}{8}, 13\dfrac{\pi}{8}$$
  • $$11\dfrac{\pi}{8}, 15\dfrac{\pi}{8}$$
  • $$15\dfrac{\pi}{8}, 19\dfrac{\pi}{8}$$
If $$2\sin^{2}\theta + \sqrt {3}\cos \theta + 1 = 0$$, then the value of $$\theta$$ is
  • $$\dfrac {\pi}{6}$$
  • $$\dfrac {2\pi}{3}$$
  • $$\dfrac {5\pi}{6}$$
  • $$\pi$$
The set of values of a for which the equation $$\sin x(\sin x+\cos x)=a$$ has real solutions is
  • $$[1-\sqrt{2}, 1+\sqrt{2}]$$
  • $$[2-\sqrt{3}, 2+\sqrt{3}]$$
  • $$[0, 2+\sqrt{3}]$$
  • $$\left[\displaystyle\frac{1-\sqrt{2}}{2}, \frac{1+\sqrt{2}}{2}\right]$$
Which one of the following equations has no solution?
  • $$\csc { \theta } -\sec { \theta } =\csc { \theta } \cdot \sec { \theta } $$
  • $$\csc { \theta } \cdot \sec { \theta } =1$$
  • $$\cos { \theta } +\sin { \theta } =\sqrt { 2 } $$
  • $$\sqrt { 3 } \sin { \theta } -\cos { \theta } =2$$
One of the principal solutions of $$ \sqrt3 \sec x = - 2 $$ is equal to :
  • $$ \dfrac {2 \pi} {3} $$
  • $$ \dfrac { \pi} {6} $$
  • $$ \dfrac {5 \pi} {6} $$
  • $$ \dfrac {\pi} {3} $$
  • $$ \dfrac {\pi} {4} $$
The equation $$4 sin^2 x - 2(\sqrt3 + 1) sinx + \sqrt3 = 0$$ has
  • $$2$$ solutions in $$(0, \pi)$$
  • $$ 4 $$ solutions in $$(0, 2 \pi)$$
  • $$ 2$$ solutions in $$(- \pi, \pi)$$
  • $$ 4$$ solutions in $$(- \pi, \pi)$$
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