CBSE Questions for Class 11 Engineering Maths Trigonometric Functions Quiz 10 - MCQExams.com

In $$\Delta ABC$$, a $$sin(B-C)+b{\,}sin (C-A)+c{\,}sin(A-B)=$$
  • $$0$$
  • $$a+b+c$$
  • $$a^2+b^2+c^2$$
  • $$2(a^2+b^2+c^2)$$
$$\sin^2 20+\sin^270$$ is equal to_____
  • $$1$$
  • $$-1$$
  • $$0$$
  • $$2$$
Let $$x$$ and $$y$$ be $$2$$ real numbers which satisfy the equations $$(\tan^{2} x - \sec^{2}y) = \dfrac {5a}{6} - 3$$ and $$(-\sec^{2}x + \tan^{2}y) = a^{2}$$, then the value of a can be equal to
  • $$\dfrac {2}{3}$$
  • $$\dfrac {-2}{3}$$
  • $$\dfrac {3}{2}$$
  • $$\dfrac {-3}{2}$$
$$ \sin (A+B) . \sin (A-B) = $$
  • $$ \sin^2 A - \cos^2 B $$
  • $$ \cos^2 A - \sin^2 B $$
  • $$ \sin^2 A - \sin^2 B $$
  • $$ \cos^2 A - \cos^2 B $$
If $$4\ \sin^{2}x-1=0$$ and $$0 < x < 2 \pi$$, then positive values of $$x$$ are 
  • $$30^{o},120^{o},210^{o},300^{o}$$
  • $$30^{o},150^{o},210^{o},330^{o}$$
  • $$30^{o},120^{o},150^{o},210^{o}$$
  • $$30^{o},160^{o},210^{o},320^{o}$$
Solution set of the equation $$\sin ^{ 2 }{ x } +\cos ^{ 2 }{ 3x }$$ =1$$ is given by 
  • $$\left\{ \frac { n\pi }{ 4 } ,n\epsilon I \right\}$$
  • $$\left\{ n\pi ,n\epsilon I \right\}$$
  • $$\left\{ \frac { n\pi }{ 2 } ,n\epsilon I \right\}$$
  • $$none of these$$
The no of solution of the equation: $$1+\sin { x } \cos { x } =2\sin { x } \cos { x } $$ in $$x$$, $$\left[ 0,40 \right] $$ are
  • $$4$$
  • $$5$$
  • $$7$$
  • $$None\ of\ these$$
If $$\sin { x } sin{ \left( { 60 }^{ O }+x \right) .\left( { 60 }^{ O }-x \right)  }=\frac { 1 }{ 8 } $$ then$$x=$$
  • $$\pi+(-1)^\alpha\frac{\pi}{6}$$
  • $$\frac{\pi}{3}+(-1)^\alpha\frac{\pi}{18}$$
  • $$n\pi \left( -1 \right) ^{ \alpha }\frac { \pi }{ 3 }$$
  • $$\frac { n\pi }{ 3 } +\left( -1 \right) ^{ \alpha }\frac { \pi }{ 9 }$$
Find number of solutions to the equation:$$\left[ \sin { x+\cos { x }  }  \right] =3+\left[ -\sin { x }  \right] +\left[ -\cos { x }  \right]$$
  • $$0$$
  • $$1$$
  • $$2$$
  • infinite
The number of solutions of the equation $$|\cot x|=\cot x+\dfrac{1}{\sin x}(0\le x\le 2\pi)$$ is :
  • $$0$$
  • $$1$$
  • $$2$$
  • $$3$$
If $$\cos 3x=-1$$, where $$0^{o} \ge x \ge 360^{o}$$, then $$x$$
  • $$60^{o},180^{o},300^{o}$$
  • $$180^{o}$$
  • $$60^{o},180^{o}$$
  • $$180^{o},300^{o}$$
If $$\theta$$ is an acute angle such that $$\sec^2 \theta = 3$$. then the value of $$\dfrac{\tan^2 \theta - \text{cosec}^2 \theta}{\tan^2 \theta - \text{cosec}^2 \theta}$$ is 
  • $$\dfrac{4}{7}$$
  • $$\dfrac{3}{7}$$
  • $$1$$
  • $$\dfrac{1}{7}$$
If $$3\sec\theta+2\sec\dfrac{\pi}{4}=2\cos\theta$$, where $$\theta\in (0, 2\pi)$$, then which of the following can be correct?
  • $$\cos 2\theta=0$$
  • $$\sin 2\theta=1$$
  • $$\tan \theta=1$$
  • $$\tan \theta=-1$$
For $$x\ \in\ (0,\pi)$$, the equation $$\sin x+2\sin 2x-\sin 3x=3$$ has
  • infinitely solutions
  • three solution
  • one solution
  • no solution
The number of value of $$x\in (0,2\pi)$$ satisfying $$\log_{\tan x}(2+4\cos^2x)=2$$
  • $$\dfrac{\pi}{4}$$
  • $$\dfrac{\pi}{2}$$
  • $$\dfrac{\pi}{3}$$
  • $$\dfrac{\pi}{6}$$
The sum $$s=sin\theta+sin2\theta+.......+sin n \theta$$, equals
  • $$sin\dfrac{1}{2}(n+1)\theta sin \dfrac{1}{2}n \theta/ sin \dfrac{\theta}{2}$$
  • $$cos\dfrac{1}{2}(n+1)\theta sin \dfrac{1}{2}n \theta/ sin \dfrac{\theta}{2}$$
  • $$sin\dfrac{1}{2}(n+1)\theta sin \dfrac{1}{2}n \theta/ cos \dfrac{\theta}{2}$$
  • $$cos\dfrac{1}{2}(n+1)\theta sin \dfrac{1}{2}n \theta/ cos\dfrac{\theta}{2}$$
If $$(1+\tan{A}).(1+\tan{B})=2$$, then $$A+B$$ is 
  • $$\dfrac{\pi}{2}$$
  • $$\dfrac{\pi}{3}$$
  • $$\dfrac{\pi}{4}$$
  • $$\dfrac{\pi}{6}$$
If $$3\sin { 2\theta  } =2\sin { 3\theta  }$$ and $$0<\theta <\pi$$, then value of  $$\sin { \theta  }$$ is 
  • $$\dfrac{\sqrt{2}}{3}$$
  • `$$\dfrac{\sqrt{3}}{\sqrt{5}}$$
  • $$\dfrac{\sqrt{15}}{4}$$
  • $$\dfrac{\sqrt{2}}{\sqrt{5}}$$
If $$\cos2x\ +\ 2\cos\ x\ =\ 1$$, then $$\sin^{2}x(2-\cos^{2}x)$$ is
  • $$1$$
  • $$2$$
  • $$4$$
  • none of these
State whether the following statement is true or false:
$$cosec{20^ \circ }\sec {20^ \circ } = $$
  • $$2$$
  • $$2 cosec {40^ \circ}$$
  • $$4$$
  • $$2\sin{45^ \circ} . cosec {40^ \circ}$$
$${ cos }^{ 2 }2x+2{ cos }^{ 2 }x=1,x\epsilon \left( -\pi ,\pi  \right)$$, then $$x$$ can take the values
  • $$\pm \dfrac { \pi }{ 2 }$$
  • $$\pm \dfrac { \pi }{ 4 }$$
  • $$\pm \dfrac { 3\pi }{ 8 }$$
  • Non of these
The number of solutions to the equation $$sin\ 5x+\ sin\ 3x\ +\ sin\ x=0$$ for $$\ 0\leq x\leq \pi$$ is
  • 1
  • 2
  • 3
  • None of these
State true or false.
$${(\cos x + {\mathop{\rm cosy}\nolimits} )^2} + {(\sin x - \sin y)^2} = 4{\cos ^2}\left( {\frac{{x + y}}{2}} \right)$$
  • True
  • False
If $$\cos^{2}x=\sin x$$, then the value of $$\cos^{2}x(1+\cos^{2}x)$$ is equal to
  • $$-1$$
  • $$1$$
  • $$0$$
  • $$\dfrac{1}{2}$$
$$\dfrac{{\sec 8{\text{A}} - 1}}{{\sec 4{\text{A}} - 1}} = $$
  • $$\dfrac{{\tan 2{\text{A}}}}{{\tan 8{\text{A}}}}$$
  • $$\dfrac{{\tan 8{\text{A}}}}{{\tan 2{\text{A}}}}$$
  • $$\dfrac{{{\text{cot8A}}}}{{\cot 2{\text{A}}}}$$
  • $$\dfrac{{{\text{tan6A}}}}{{\tan 2{\text{A}}}}$$
If $$\tan \theta + \, \cot \theta = 4$$, then the value of $$\tan^3 \theta + \cot^3 \theta$$ is 
  • $$52$$
  • $$16$$
  • $$7 \dfrac{9}{8}$$
  • $$27 \dfrac{1}{27}$$
The positive integer value of $$n>3$$ satisfing the equation
 $$\frac{1}{{\sin \left( {\frac{\pi }{n}} \right)}} = \frac{1}{{\sin \left( {\frac{{2\pi }}{n}} \right)}} + \frac{1}{{\sin \left( {\frac{{3\pi }}{n}} \right)}}$$
 is 
  • $$7$$
  • $$8$$
  • $$9$$
  • $$10$$
If $$cot\Theta =sin2\Theta (where\Theta \neq n\pi ,n\ is\ an\ integer)\Theta $$=
  • 45$$^{0}$$ and 60$$^{0}$$
  • 45 $$^{0}$$ and 90 $$^{0}$$
  • only 45$$^{0}$$
  • only 90$$^{0}$$
$$(\sec\ A-\cos\ A)(\sec\ A+\cos\ A)=\sin^{2}\ A+\tan^{2}A$$.
  • True
  • False
In a triangle ABC,
 $$b\,cos\,(C+\theta)+c\,cos(B-\theta)=$$
  • $$a\,cos\,\theta$$
  • $$a\,sin\,\theta$$
  • $$a\,tan\,\theta$$
  • $$a\,cot\,\theta$$
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