CBSE Questions for Class 10 Maths Introduction To Trigonometry Quiz 12 - MCQExams.com

If $$\cos 9\theta=\sin \dfrac{\pi}{4}$$, then the value of $$\tan 6\theta$$ is
  • $$\dfrac {1}{\sqrt {3}}$$
  • $$\sqrt {3}$$
  • $$1$$
  • $$0$$
If $$\tan { x } =3\cot { x } ,$$ then x =?
  • $${ 45 }^{ \circ }$$
  • $${ 60 }^{ \circ }$$
  • $${ 30 }^{ \circ }$$
  • $${ 15 }^{ \circ }$$
$$\cos 35 ^ { \circ } + \cos 85 ^ { \circ } + \cos 155 ^ { \circ }$$ is
  • 0
  • $$\frac { 1 } { \sqrt { 3 } }$$
  • $$\frac { 1 } { \sqrt {2 } }$$
  • $$\cos 275 ^ { \circ }$$
$${cos}^{2}0+{cos}^{2}10+{cos}^{2}20+{cos}^{2}30+{cos}^{2}40+{cos}^{2}50+{cos}^{2}60+{cos}^{2}70+{cos}^{2}80+{cos}^{2}90=$$
  • $$0$$
  • $$1$$
  • $$5$$
  • $$10$$
If $$\sin \theta = \cos \theta$$, then $$\theta = ?$$
  • $$45^{o}$$
  • $$90^{o}$$
  • $$0^{o}$$
  • $$30^{o}$$
$$\cot{1^0}\cot{2^0}\cot{3^0}\cot{4^0}...\cot{89^0}$$.
  • 1
  • 0
  • -1
  • NONE OF THE GIVEN
Choose the correct alternative:
$$\ cosec \theta = \dfrac { 1 } { \dots \ldots }$$
  • $$\cos \theta$$
  • $$\sin \theta$$
  • $$\tan \theta$$
  • $$\cot \theta$$
Consider the following statements : 
$$\cos\theta+\sec\theta$$ can never be equal to $$1.5$$
$$\tan\theta+\cot\theta$$ can never be less than to $$2$$
Which of the above statements is/are correct ?
  • $$1$$ only
  • $$2$$ only
  • Both $$1$$ and $$2$$
  • Neither $$1$$ nor $$2$$
If $$\sin A+\cos A= {\sqrt2}$$ and $$\tan A+\cot A=2$$, then the value of $$\sec A\cdot \csc A$$ is equal to 
  • $$2$$
  • $$3$$
  • $$4$$
  • $$\dfrac{1}{2}$$
If x is acute, then $$\displaystyle \sqrt{\frac{1 + sin x}{1 - sin x}} = ?$$
  • $$\displaystyle sec x + cosec x$$
  • $$\displaystyle sec x + tan x$$
  • $$\displaystyle cosec x + cot x$$
  • $$\displaystyle tan x + cot x$$
If $$\displaystyle  \tan \theta + \cot \theta = 2$$, then $$\displaystyle  \sin \theta = $$?
  • $$\displaystyle \frac{1}{2}$$
  • $$\displaystyle \frac{1}{\sqrt{2}}$$
  • $$\displaystyle \frac{\sqrt{3}}{2}$$
  • $$\displaystyle \frac{1}{\sqrt{3}}$$
$$\displaystyle (sec \theta - cos \theta) (cosec \theta - sin \theta) (cot \theta + tan \theta) = ?$$
  • $$\displaystyle 1$$
  • $$\displaystyle -1$$
  • $$\displaystyle 0$$
  • none of these
$$\displaystyle \Bigg( \frac{\sec \theta + \tan \theta - 1}{\tan \theta - \sec \theta + 1} \Bigg)^2 = $$  ?
  • $$\displaystyle \frac{ ( 1 + \sin \theta)}{1-\sin\theta)}$$
  • $$\displaystyle \frac{ ( 1 - \sin \theta)}{1+\sin\theta)}$$
  • $$\displaystyle 1$$
  • none of these
If $$ \displaystyle \cos^2 \theta + sec^2 \theta = p$$, then
  • $$ \displaystyle p < 1 $$
  • $$ \displaystyle p = 1 $$
  • $$ \displaystyle 1 < p < 2$$
  • $$ \displaystyle p \geq 2$$
If $$\displaystyle \sin \theta + \sin^2 \theta = 1$$, then $$\displaystyle (\cos^2 \theta + \cos^4 \theta) = $$?
  • $$\displaystyle 0$$
  • $$\displaystyle 1$$
  • $$\displaystyle 2$$
  • none of these
$$\displaystyle sin \theta \left(\frac{sin\theta}{1 + cos \theta} + \frac{1 + cos \theta}{sin \theta}\right) = ?$$
  • $$\displaystyle 1$$
  • $$\displaystyle 2$$
  • $$\displaystyle 3$$
  • $$\displaystyle 4$$
If $$\theta =30^o$$, then $$\dfrac{1-\sin^22\theta}{\cos 2\theta}$$ is
  • $$1$$
  • $$-1$$
  • $$2$$
  • $$-2$$
$$ \dfrac{1}{cosec \theta - \cot \theta} $$ is equal to:
  • $$ cosec \theta + \cot \theta $$
  • $$ \dfrac{1}{cosec \theta + \cot \theta} $$
  • $$ cosec \theta - \cot \theta $$
  • $$ \tan \theta $$

If $$a \sin^{2}x+b\cos^{2}x=c, b\sin^{2}y+a\cos^{2}y=d$$ and $$a \tan x=b\tan y,$$ then $$\displaystyle \frac{a^{2}}{b^{2}}$$ equals to
  • $$^{\displaystyle \frac{(a-d)(c-a)}{(b-c)(d-b)}}$$
  • $$^{\displaystyle \frac{(b-c)(b-d)}{(a-c)(a-d)}}$$
  • $$\displaystyle \frac{(b-c)(d-b)}{(a-d)(c-a)}$$
  • $$^{\displaystyle \frac{(d-a)(c-a)}{(b-c)(d-b)}}$$
If $$\dfrac {\sin\alpha}{\sin\beta}=\dfrac {\sqrt 3}{2}$$ and $$\dfrac {\cos\alpha}{\cos\beta}=\dfrac {\sqrt 5}{2}, 0 < \alpha < \beta < \dfrac {\pi}{2}$$, then
  • $$\tan\alpha=1$$
  • $$\tan\alpha=\dfrac {\sqrt 3}{\sqrt 5}$$
  • $$\tan\beta=\dfrac {\sqrt 3}{\sqrt 5}$$
  • $$\tan\beta=1$$
The value of the expression $$(\tan1^{0} \tan2^{0} \tan 3^{0}...\tan89^{0})$$ is equal to
  • $$0$$
  • $$1$$
  • $$2$$
  • $$\dfrac{1}{2}$$
If $$\cos9 \alpha= \sin \alpha$$ and $$9 \alpha < 90^{0}$$, then the value of $$\tan5 \alpha$$ is
  • $$\dfrac{1}{\sqrt{3}}$$
  • $$\sqrt{3}$$
  • $$1$$
  • $$0$$

 lf $$x=\displaystyle \frac{\sin^{3}p}{\cos^{2}p}, y=\displaystyle \frac{\cos^{3}p}{\sin^{2}p}$$ and $$\displaystyle \sin p+\cos p=\frac{1}{2}$$, then $$x+y=$$
  • $$\dfrac {75}{18}$$
  • $$\dfrac{44}9$$
  • $$\dfrac {79}{18}$$
  • $$\dfrac {48}9$$

$$\displaystyle {x}=\frac{\sin^{3}{p}}{\cos^{2}{p}}, \displaystyle {y}=\frac{\cos^{3}{p}}{\sin^{2}{p}}$$ and $$\sin p$$ $$+$$ $$\cos p $$ $$= \dfrac 12$$ then $${x}+{y}=$$
  • $$\displaystyle \frac{75}{18}$$
  • $$\displaystyle \frac{44}{9}$$
  • $$\displaystyle \frac{79}{18}$$
  • $$\displaystyle \frac{48}{9}$$
If $$\sin x+\sin ^{2}x=1$$,then the value of $$\cos ^{12}x+3\cos ^{10}x+3\cos ^{8}x+\cos ^{6}x-2$$ is equal to
  • $$0$$
  • $$1$$
  • $$-1$$
  • $$2$$
$$\cos\theta +\cos^{2}\theta =1$$ and $$a\sin^{12}\theta +b\sin^{10}\theta +c\sin^{8}\theta +d\sin^{6}\theta =1.$$ Then $$\displaystyle \frac{b+c}{a+d}=$$?
  • $$2$$
  • $$3$$
  • $$4$$
  • $$6$$
If $$a \sin^{2}\theta+b\cos^{2}\theta=a\cos^{2}\phi+b\sin^{2}\phi=1$$ and $$a \tan\theta=b\tan\phi$$, then choose the correct option.
  • $${a+b}=2ab$$
  • $${a-b}=2ab$$
  • $${a-b}+2ab=0$$
  • $${a+b}+2ab=0$$
lf $$a \sin \theta + b \cos \theta = c$$, then $$\dfrac {a - b \tan \theta}{b + a \tan \theta} =$$
  • $$\dfrac {\sqrt {a^{2}+b^{2}-c^{2}}}{c}$$
  • $$-\dfrac {\sqrt {a^{2}+b^{2}-c^{2}}}{c}$$
  • $$\displaystyle \pm \dfrac {\sqrt {a^{2}+b^{2}-c^{2}}}{c}$$
  • $$\displaystyle \pm\dfrac {\sqrt {a^{2}+b^{2}+c^{2}}}{c}$$
$$\cfrac { \cos { \theta  }  }{ 1-\sin { \theta  }  } -\cfrac { \cos { \theta  }  }{ 1+\sin { \theta  }  } =2$$ is satisfied by which one of the following values of $$\theta$$?
  • $$\cfrac { \pi }{ 2 } $$
  • $$\cfrac { \pi }{ 3 } $$
  • $$\cfrac { \pi }{ 4 } $$
  • $$\cfrac { \pi }{ 6 } $$
If $$\tan { \theta  } =\cfrac { p }{ q } $$, then what is $$\cfrac { p\sec { \theta  } -qco\sec { \theta  }  }{ p\sec { \theta  } +qco\sec { \theta  }  } $$ equal to?
  • $$\cfrac { p-q }{ p+q } $$
  • $$\cfrac { { q }^{ 2 }-{ p }^{ 2 } }{ { q }^{ 2 }+{ p }^{ 2 } } $$
  • $$\cfrac { { p }^{ 2 }-{ q }^{ 2 } }{ { q }^{ 2 }+{ p }^{ 2 } } $$
  • $$1$$
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