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Quantitative Aptitude

TRIGONOMETRY MCQs

Total Questions : 420 | Page 12 of 42 pages
Question 111. $$\frac{{{\text{cos }}\alpha }}{{{\text{sin }}\beta }} = n$$   and $$\frac{{{\text{cos }}\alpha }}{{{\text{cos }}\beta }} = m,$$   then the value of $${\text{co}}{{\text{s}}^2}\beta $$   is?
  1.    $$\frac{{{m^2} - 1}}{{{n^2} - 1}}$$
  2.    $$\frac{{{m^2} - 3}}{{{n^2} - 4}}$$
  3.    $$\frac{{{m^2} + 3}}{{{n^2} + 3}}$$
  4.    $$\frac{{{n^2}}}{{{m^2} + {n^2}}}$$
 Discuss Question
Answer: Option D. -> $$\frac{{{n^2}}}{{{m^2} + {n^2}}}$$
Question 112. If tanθ + cotθ = 5, then tan2θ + cot2θ is?
  1.    23
  2.    24
  3.    25
  4.    26
 Discuss Question
Answer: Option A. -> 23
Question 113. If tanA = n tanB and sinA = m sinB, then the value of cos2A = ?
  1.    $$\frac{{{m^2} + 1}}{{{n^2} + 1}}$$
  2.    $$\frac{{{m^2} + 1}}{{{n^2} - 1}}$$
  3.    $$\frac{{{m^2} - 1}}{{{n^2} - 1}}$$
  4.    $$\frac{{{m^2} - 1}}{{{n^2} + 1}}$$
 Discuss Question
Answer: Option C. -> $$\frac{{{m^2} - 1}}{{{n^2} - 1}}$$
Question 114. The value of tan 4°.tan 43°.tan 47°.tan 86° is?
  1.    2
  2.    3
  3.    1
  4.    4
 Discuss Question
Answer: Option C. -> 1
Question 115. The value of tan 1°.tan 2°.tan 3° ............. tan 89° is?
  1.    1
  2.    0
  3.    $$\sqrt 3 $$
  4.    $$\frac{1}{{\sqrt 3 }}$$
 Discuss Question
Answer: Option A. -> 1
Question 116. The value of cot 10°.cot 20°.cot 60°.cot 70°.cot 80° is?
  1.    1
  2.    -1
  3.    $$\sqrt 3 $$
  4.    $$\frac{1}{{\sqrt 3 }}$$
 Discuss Question
Answer: Option D. -> $$\frac{1}{{\sqrt 3 }}$$
Question 117. The value of cot 18° $$\left( {{\text{cot 7}}{{\text{2}}^ \circ }{\text{.co}}{{\text{s}}^2}{{22}^ \circ } + \frac{1}{{{\text{tan 7}}{{\text{2}}^ \circ }.{\text{se}}{{\text{c}}^2}{{68}^ \circ }}}} \right)$$      is?
  1.    1
  2.    $$\sqrt 2 $$
  3.    3
  4.    $$\frac{1}{{\sqrt 3 }}$$
 Discuss Question
Answer: Option A. -> 1
Question 118. If x, y are acute angles, 0 < x + y < 90° and sin(2x - 20°) = cos(2y + 20°), then the value of tan(x + y) is?
  1.    $$\frac{1}{{\sqrt 3 }}$$
  2.    $$\frac{{\sqrt 3 }}{2}$$
  3.    $$\sqrt 3 $$
  4.    1
 Discuss Question
Answer: Option D. -> 1
Question 119. Sin25° + sin26° + ............. sin284° + sin285° = ?
  1.    $$30\frac{1}{2}$$
  2.    $$40\frac{1}{2}$$
  3.    40
  4.    $$39\frac{1}{2}$$
 Discuss Question
Answer: Option B. -> $$40\frac{1}{2}$$
Question 120. Sin25° + sin210° + sin215° + ...... sin285° + sin290° is equal to?
  1.    $${\text{7}}\frac{1}{2}$$
  2.    $${\text{8}}\frac{1}{2}$$
  3.    9
  4.    $$9\frac{1}{2}$$
 Discuss Question
Answer: Option D. -> $$9\frac{1}{2}$$

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