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Quantitative Aptitude

TRIGONOMETRY MCQs

Total Questions : 420 | Page 7 of 42 pages
Question 61. If $$\sqrt 3 $$ tanθ = 3sinθ, then the value of (sin2θ - cos2θ) is?
  1.    1
  2.    3
  3.    $$\frac{1}{3}$$
  4.    None of these
 Discuss Question
Answer: Option C. -> $$\frac{1}{3}$$
Question 62. If sinθ = $$\frac{a}{b}$$  then the value of secθ - cosθ is? (where 0° < θ < 90°)
  1.    $$\frac{a}{{b\sqrt {{b^2} - {a^2}} }}$$
  2.    $$\frac{{{b^2}}}{{a\sqrt {{b^2} - {a^2}} }}$$
  3.    $$\frac{{{a^2}}}{{b\sqrt {{b^2} - {a^2}} }}$$
  4.    $$\frac{{\sqrt {{b^2} + {a^2}} }}{{\sqrt {{b^2} - {a^2}} }}$$
 Discuss Question
Answer: Option C. -> $$\frac{{{a^2}}}{{b\sqrt {{b^2} - {a^2}} }}$$
Question 63. If secα + tanα = 2, then the value of sinα is (assume that 0 < α < 90°)
  1.    0.4
  2.    0.5
  3.    0.6
  4.    0.8
 Discuss Question
Answer: Option C. -> 0.6
Question 64. If $$sec\theta = x + \frac{1}{{4x}}$$   $$\left( {{0^ \circ } < \theta < {{90}^ \circ }} \right)$$   then $$sec\theta $$  + $${\text{tan}}\theta $$   is equal to?
  1.    $$\frac{x}{2}$$
  2.    2x
  3.    x
  4.    $$\frac{1}{{2x}}$$
 Discuss Question
Answer: Option B. -> 2x
Question 65. If secθ + tanθ = 2 + $$\sqrt 5 {\text{,}}$$  then the value of sinθ + cosθ is?
  1.    $$\frac{3}{{\sqrt 5 }}$$
  2.    $$\sqrt 5 $$
  3.    $$\frac{7}{{\sqrt 5 }}$$
  4.    $$\frac{1}{{\sqrt 5 }}$$
 Discuss Question
Answer: Option A. -> $$\frac{3}{{\sqrt 5 }}$$
Question 66. If A is an acute angle and cotA + cosecA = 3, then the value of sinA is?
  1.    1
  2.    $$\frac{4}{5}$$
  3.    $$\frac{3}{5}$$
  4.    0
 Discuss Question
Answer: Option C. -> $$\frac{3}{5}$$
Question 67. If θ is positive acute angle and 3(sec2θ + tan2θ) = 5, then the value of cos2θ is?
  1.    $$\frac{1}{2}$$
  2.    $$\frac{{\sqrt 3 }}{2}$$
  3.    $$\frac{1}{{\sqrt 2 }}$$
  4.    1
 Discuss Question
Answer: Option A. -> $$\frac{1}{2}$$
Question 68. If the sum and difference of two angles are 135° and $$\frac{\pi }{{12}}$$  respectively, then the value of the angles in degree measure are?
  1.    70°, 65°
  2.    75°, 60°
  3.    45°, 90°
  4.    80°, 55°
 Discuss Question
Answer: Option B. -> 75°, 60°
Question 69. If cosx + cos2x = 1,the numerical value of (sin12 + 3sin10x + 3sin8x + sin6x - 1) = ?
  1.    -1
  2.    2
  3.    0
  4.    1
 Discuss Question
Answer: Option C. -> 0
Question 70. If cosθ + sinθ = $$\sqrt 2 $$ cosθ, then cosθ - sinθ is?
  1.    $$\sqrt 2 $$ tanθ
  2.    -$$\sqrt 2 $$ cosθ
  3.    -$$\sqrt 2 $$ sinθ
  4.    $$\sqrt 2 $$ sinθ
 Discuss Question
Answer: Option D. -> $$\sqrt 2 $$ sinθ

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