CBSE Questions for Class 11 Engineering Maths Trigonometric Functions Quiz 2 - MCQExams.com

The value of $$\operatorname { \sec } ^ { 2 } A \operatorname { \tan } ^ { 2 } B - \tan ^ { 2 } A \operatorname { \sec } ^ { 2 } B $$ is
  • $$\operatorname { \tan } ^ { 2 } B - \tan ^ { 2 } A$$
  • $$\operatorname { \sec } ^ { 2 } B + \operatorname { \sec } ^ { 2 } A$$
  • $$\tan ^ { 2 } B - \operatorname { \sec } ^ { 2 } A$$
  • $$\operatorname { \sec } ^ { 2 } B - \tan ^ { 2 } A$$
Which of the following is the principal value of $$\cos { ^{ -1 }\left( \dfrac { -1 }{ 2 }  \right)  } $$?
  • $$\dfrac { \pi }{ 3 } $$
  • $$\dfrac { \pi }{ 6 } $$
  • $$\dfrac { 2\pi }{ 3 } $$
  • $$\dfrac { 3\pi }{ 3 } $$
If $$cos x=b$$, then for what b do the roots of the equation form an AP ?
  • $$-1$$
  • $$\cfrac { 1 }{ 2 } $$
  • $$\cfrac { \sqrt { 3 } }{ 2 } $$
  • None of these
 The principle solutions of $$\sin \theta  =  - \frac{1}{2}$$ are
  • $$\pi /4$$
  • $$11\pi /6$$
  • $$\pi /3$$
  • $$\frac{{7\pi }}{6}$$
$$ \sin A(1+\tan A) + \cos A(1+\cot A) = \sec A + \text{cosec} A.$$
  • True
  • False
$$\dfrac{\cos(90-A)\sin(90-A)}{\tan (90-A)}$$=
  • $$\sin^{2}A$$
  • $$\cos^{2}A$$
  • $$\sin A$$
  • $$1$$
The principle solution of the $$Cos\theta  =  - \frac{1}{2}$$ is 
  • $$2\pi /3$$
  • $$\pi /6$$
  • $$ 4\pi /3$$
  • $$\frac{{7\pi }}{6}$$
$$\sec^{2} A+ \csc^{2} A=\sec^{2} A \csc^{2} A$$
  • True
  • False
What is the value of $$\cfrac{\tan{A}-\sin{A}}{\sin^3{A}}$$?
  • $$\cfrac{\sec{A}}{1-\cos{A}}$$
  • $$\cfrac{\sec{A}}{1+\cos^2{A}}$$
  • $$\cfrac{\sec{A}}{1+\cos{A}}$$
  • None of these
The principle solution of equation $$\cot x =  - \sqrt 3 $$ is 
  • $$\dfrac{\pi }{3}$$
  • $$\dfrac{2\pi }{3}$$
  • $$\dfrac{\pi }{6}$$
  • $$\dfrac{5\pi }{6}$$
The range of the function $$f(x)=\left (\cos ^2x+4\sec ^2x\right )$$ is
  • $$[4,\infty )$$
  • $$[0,\infty )$$
  • $$[5,\infty )$$
  • $$(0,\infty )$$
$$\displaystyle 1^c =?$$
  • $$\displaystyle 56^027'22''$$
  • $$\displaystyle 57^016'22''$$
  • $$\displaystyle 55^018'32''$$
  • $$\displaystyle 57^026'32''$$
If tan $$\theta =\dfrac{1}{\sqrt{5}}$$ and $$\theta$$ lies in the first quadrant, the value of $$\cos\theta$$ is
  • $$\dfrac{1}{\sqrt{6}}$$
  • $$\dfrac{\sqrt{5}}{\sqrt{6}}$$
  • $$\dfrac{-1}{\sqrt{6}}$$
  •  $$\dfrac{-\sqrt{5}}{\sqrt{6}}$$
If $$0^0 < x < 45^0,$$ then consider the following statements :

Assertion (A):

$$\dfrac{1}{1+sin^{2} x}-\dfrac{1}{1+sec^{2} x}\neq \dfrac{1}{1+cos^{2} x}-\dfrac{1}{1+cosec^{2}x}$$

Reason (R) : $$ sin x \neq cos x$$

of these statements :
  • Both A and R are true and R is the correct explanation of A
  • Both A and R are true, but R is not the correct explanation of A.
  • A is true, but R is false.
  • A is false, but R is true.
$$1)$$ Principal value of $$\cos\theta=-1$$ is $$\pi$$
$$2)$$ Principal value of $$\sin\theta=0$$ is $$\pi$$
Which of the above statement is correct?
  • Only I
  • Only II
  • Both I and II
  • Neither I or II
Let $$n$$ be a positive integer such that
$$\displaystyle \sin(\frac{\pi}{2^{n}})+\cos(\frac{\pi}{2^{n}})=\frac{\sqrt{n}}{2}$$ 
  • $$<4$$
  • $$n>8$$
  • $$4\leq n<8$$
  • $$6\leq n\leq 8$$

If $$\mathrm{p}_{1}, \mathrm{p}_{2}, \mathrm{p}_{3}$$ are the principal values of following trigonometric equations
1)$$\sin\theta=-\dfrac 1{\sqrt{2}}$$
2)$$\displaystyle \cos\theta=-\frac{\sqrt{3}}{2}$$
3)$$\tan\theta=\sqrt{3}-2$$
  • $$p_{1}< p_{2}< p_{3}$$
  • $$p_{1}< p_{3}< p_{2}$$
  • $$p_{3}< p_{1}< p_{2}$$
  • $$p_{2}< p_{3}< p_{1}$$

The number of solutions of the equation $$8{\tan ^2}\theta  + 9 = 6\sec \theta $$ in the interval $$(\frac{-\pi}{2}, \frac{\pi}{2})$$
  • Two
  • Four
  • Zero
  • None of these
lf $$\alpha$$ and $$\beta$$ are two different solutions lying between $$\displaystyle \frac{-\pi}{2}$$ and $$\displaystyle \frac{\pi}{2}$$ of the equation $$2t\mathrm{a}n\theta+\mathrm{S}\mathrm{e}\mathrm{c}\theta=2$$ then $$ t\mathrm{a}n\alpha+t\mathrm{a}n\beta$$ 
  • 0
  • 1
  • 4/3
  • 8/3
For all values of $$\theta,\cos\theta.\text{cosec }\theta\sqrt{\sec^2\theta-1}$$ is
  • $$1$$
  • $$\cos^2\theta$$
  • $$\cot\theta$$
  • $$\tan\theta$$
If $$ sec \theta - tan \theta=k,$$ then the value of $$ sec \theta + tan \theta$$ is
  • $$(1 - k)$$
  • $$(1+k)$$
  • $$\dfrac{1}{k}$$
  • $$1-\dfrac{1}{k}$$
Which of the following is/are FALSE   $$\forall \theta \in R$$?
  • $$\sin \theta =1 - \cos \theta$$
  • $$\sec \theta - \tan \theta =\dfrac{1}{\sec \theta + \tan \theta}$$
  • $$\tan^2 \theta - \sin^2 \theta = \tan^2 \theta \sin^2 \theta$$
  • $$\sin \dfrac{\pi}{3}=\cos\dfrac{\pi}{6}$$
If $$\tan\theta=\dfrac{3}{4}$$ and $$0< \theta, < 90^0,$$ then the value of $$\sin\theta \cos \theta$$ is
  • $$\dfrac{1}{5}$$
  • $$\dfrac{9}{5}$$
  • $$\dfrac{12}{25}$$
  • $$\dfrac{25}{12}$$
$$\dfrac{3-4 \sin^2 \theta}{\cos^2 \theta}$$ is equal to
  • $$3 - \cot^2 \theta$$
  • $$3 + \cot^2 \theta$$
  • $$3 - \tan^2 \theta$$
  • $$3+ \tan^2 \theta$$
The value of $$(\cos \theta + \sin \theta)^2 + (\cos \theta - \sin \theta)^2$$ is
  • $$0$$
  • $$1$$
  • $$2$$
  • $$3$$
$$\dfrac{\tan^{2}\theta}{(1+\sec \theta)^{2}}$$ is equal to
  • $$\left ( \dfrac{1-\cos \theta}{1+\cos \theta} \right )$$
  • $$\left ( \dfrac{1+\cos \theta}{1-\cos \theta} \right )$$
  • $$\left ( \dfrac{\cos \theta-1}{\cos \theta+1} \right )$$
  • $$\left ( \dfrac{\cos \theta+1}{\cos \theta-1} \right )$$
$$\sec^2 \theta +\text{cosec}^2 \theta$$ is equal to
  • $$\sec^2 \theta. \cot^2 \theta$$
  • $$\sec^2\theta. \tan^2 \theta$$
  • $$\text{cosec}^2 \theta. \cot^2 \theta$$
  • $$\sec^2 \theta. \text{cosec}^2 \theta$$
The expression $$\sin^6 \theta+\sin^4 \theta \cos^2 \theta - \sin^2 \theta \cos^4 \theta - \cos^6 \theta$$ can be reduced to
  • $$\sin^2 \theta + \cos^2 \theta$$
  • $$\sin^3 \theta - \cos^3 \theta$$
  • $$ \sin^4 \theta + \cos^4 \theta$$
  • $$\sin^2 \theta -\cos^2 \theta$$
Which of the following statements is not correct? 
  • $$cos^4 \theta sin^4 \theta - cos^2 \theta - sin^2 \theta$$
  • $$1+tan^2 \theta = sec^2 \theta$$
  • $$sin 40^0 + cos50^0 = 2 sin 40^0$$
  • $$sin^2 \theta + cos^2 \theta=2$$
The value of $$ \cos^4\theta-\sin^4 \theta+2 \sin^2 \theta$$ is equal to 
  • $$0$$
  • $$\sin^2 \theta$$
  • $$\cos^2\theta$$
  • $$1$$
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