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Quantitative Aptitude

TRIGONOMETRY MCQs

Total Questions : 420 | Page 11 of 42 pages
Question 101. If tan2θ = 1 - e2, then the value of secθ + tan3θ.cosecθ is?
  1.    $${\left( {2 + {e^2}} \right)^2}$$
  2.    $${\left( {2 - {e^2}} \right)^{\frac{1}{2}}}$$
  3.    $${\left( {2 + {e^2}} \right)^{\frac{1}{2}}}$$
  4.    $${\left( {2 - {e^2}} \right)^{\frac{3}{2}}}$$
 Discuss Question
Answer: Option D. -> $${\left( {2 - {e^2}} \right)^{\frac{3}{2}}}$$
Question 102. If $$\frac{{{\text{cos }}\alpha }}{{{\text{cos }}\beta }} = a$$   and $$\frac{{{\text{sin }}\alpha }}{{{\text{sin }}\beta }} = b{\text{,}}$$   then the value of $${\sin ^2}\beta $$  in terms of a and b is?
  1.    $$\frac{{{a^2} + 1}}{{{a^2} - {b^2}}}$$
  2.    $$\frac{{{a^2} - {b^2}}}{{{a^2} + {b^2}}}$$
  3.    $$\frac{{{a^2} - 1}}{{{a^2} - {b^2}}}$$
  4.    $$\frac{{{a^2} - 1}}{{{a^2} + {b^2}}}$$
 Discuss Question
Answer: Option C. -> $$\frac{{{a^2} - 1}}{{{a^2} - {b^2}}}$$
Question 103. The value of $${\sec ^2}\theta $$  - $$\frac{{{{\sin }^2}\theta - 2{{\sin }^4}\theta }}{{{\text{2co}}{{\text{s}}^4}\theta - {\text{co}}{{\text{s}}^2}\theta }}$$   is?
  1.    1
  2.    2
  3.    -1
  4.    0
 Discuss Question
Answer: Option A. -> 1
Question 104. Sinθ = 0.7 then cosθ, 0 ≤ θ < 90° is?
  1.    0.3
  2.    $$\sqrt {0.49} $$
  3.    $$\sqrt {0.51} $$
  4.    $$\sqrt {0.9} $$
 Discuss Question
Answer: Option C. -> $$\sqrt {0.51} $$
Question 105. If $${\text{2}}\sin \theta + {\text{cos}}\theta = \frac{7}{3}{\text{,}}$$    then the value of $$\left( {{\text{ta}}{{\text{n}}^2}\theta - {{\sec }^2}\theta } \right)$$   is?
  1.    0
  2.    -1
  3.    $$\frac{3}{7}$$
  4.    $$\frac{7}{3}$$
 Discuss Question
Answer: Option B. -> -1
Question 106. $$\sqrt {\frac{{1 + {\text{sin }}\theta }}{{1 - {\text{sin }}\theta }}} $$    + $$\sqrt {\frac{{1 - {\text{sin }}\theta }}{{1 + {\text{sin }}\theta }}} $$    is equal to?
  1.    2cosθ
  2.    2sinθ
  3.    2cotθ
  4.    2secθ
 Discuss Question
Answer: Option D. -> 2secθ
Question 107. If $${\left( {r\cos \theta - \sqrt 3 } \right)^2}$$    + $${\left( {r\sin \theta - 1} \right)^2}$$   = 0, then the value of $$\frac{{r\tan \theta + \sec \theta }}{{r\sec \theta + \tan \theta }}$$   is equal to?
  1.    $$\frac{4}{5}$$
  2.    $$\frac{3}{5}$$
  3.    $$\frac{{\sqrt 3 }}{4}$$
  4.    $$\frac{{\sqrt 5 }}{4}$$
 Discuss Question
Answer: Option A. -> $$\frac{4}{5}$$
Question 108. Let A, B, C, D be the angles of a quadrilateral. If they are concyclic, then the value of cos A + cos B + cos C + cos D is ?
  1.    0
  2.    1
  3.    -1
  4.    2
 Discuss Question
Answer: Option A. -> 0
Question 109. If $$\frac{{{\text{sec}}\theta + {\text{tan}}\theta }}{{{\text{sec}}\theta - {\text{tan}}\theta }} = 2\frac{{51}}{{79}}{\text{,}}$$     then the value of $$\sin \theta $$  is?
  1.    $$\frac{{91}}{{144}}$$
  2.    $$\frac{{39}}{{72}}$$
  3.    $$\frac{{65}}{{144}}$$
  4.    $$\frac{{35}}{{72}}$$
 Discuss Question
Answer: Option C. -> $$\frac{{65}}{{144}}$$
Question 110. If 1 + cos2θ = 3sinθ cosθ, then the integral value of cotθ is $$\left( {0 < \theta < \frac{\pi }{2}} \right) = \,?$$
  1.    2
  2.    1
  3.    3
  4.    0
 Discuss Question
Answer: Option B. -> 1

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