Trigonometry MCQ

Test your knowledge with important Trigonometry MCQ and their applications. These MCQs are beneficial for competitive exams too. Explore 30 + more Trigonometry MCQs at Bissoy

• The value of sin²64° + cos64°sin26° + 2cos43°cosec47° is:
  ক

  4

  খ

  2

  গ

  1

  ঘ

  3
• What is the value of (1 + cot²θ)(1 - cos²θ).
  ক

  1

  খ

  Can not defined

  গ

  0

  ঘ

  $$\frac{1}{2}$$
• If cotθ = √7, then the value of $$\frac{{{\text{cose}}{{\text{c}}^2}\theta - {{\sec }^2}\theta }}{{{\text{cose}}{{\text{c}}^2}\theta + {{\sec }^2}\theta }}$$   is:
  ক

  $$\frac{3}{4}$$

  খ

  $$\frac{2}{3}$$

  গ

  $$\frac{8}{9}$$

  ঘ

  $$\frac{7}{9}$$
• Using the measurements given in the following figure, the value of $$\frac{{\sin \phi + \tan \theta }}{{\sin \phi - \tan \theta }}$$   is . . . . . . . .<br><img src="/images/question-image/arithmetic-ability/trigonometry/1706088085-544.png" title="Trigonometry mcq question image" alt="Trigonometry mcq question image">
  ক

  $$ - \frac{{67}}{{37}}$$

  খ

  $$\frac{6}{{35}}$$

  গ

  $$ - \frac{7}{{32}}$$

  ঘ

  $$\frac{7}{3}$$
• If 3tanθ = 2√3sin, 0°
  ক

  $$\frac{4}{{13}}$$

  খ

  $$\frac{{20}}{{27}}$$

  গ

  $$\frac{{20}}{{39}}$$

  ঘ

  $$\frac{4}{3}$$
• The value of sin²30°.cos²45° + 2tan²30° - sec²60° is equal to:
  ক

  $$ - \frac{{13}}{{12}}$$

  খ

  $$ - \frac{{77}}{{24}}$$

  গ

  $$ - \frac{{25}}{{12}}$$

  ঘ

  $$ - \frac{1}{{12}}$$
• In ΔABC, right-angled at B, AB = 7 cm and AC - BC = 1 cm. Find the value of sinC.
  ক

  $$\frac{3}{7}$$

  খ

  $$\frac{{12}}{{13}}$$

  গ

  $$\frac{3}{{25}}$$

  ঘ

  $$\frac{7}{{25}}$$
• If sec²θ + tan²θ = $$3\frac{1}{2},$$  0°
  ক

  $$\frac{{1 + \sqrt 5 }}{3}$$

  খ

  $$\frac{{2 + \sqrt 5 }}{3}$$

  গ

  $$\frac{{1 + \sqrt 5 }}{6}$$

  ঘ

  $$\frac{{9 + 2\sqrt 5 }}{6}$$
• Evaluate the following:<br>$$\frac{{\cos 2\theta \cdot \cos 3\theta - \cos 2\theta \cdot \cos 7\theta + \cos \theta \cdot \cos 10\theta }}{{\sin 4\theta \cdot \sin 3\theta - \sin 2\theta \cdot \sin 5\theta + \sin 4\theta \cdot \sin 7\theta }}$$
  ক

  cot6θ.cot5θ

  খ

  cos6θ.cos5θ

  গ

  cos6θ.cot5θ

  ঘ

  -cot6θ.cot5θ
• If tanθ + secθ = 7, θ being acute, then the value of 5sinθ is:
  ক

  $$\frac{{25}}{{24}}$$

  খ

  $$\frac{{24}}{{25}}$$

  গ

  $$\frac{1}{{24}}$$

  ঘ

  $$\frac{{24}}{5}$$
• The value of $$\sqrt {{{\sec }^2}\theta + {\text{cose}}{{\text{c}}^2}\theta } \times \sqrt {{{\tan }^2}\theta - {{\sin }^2}\theta } $$       is equal to:
  ক

  cosecθsec²θ

  খ

  sinθsec²θ

  গ

  sinθcos²θ

  ঘ

  cosecθcos²θ
• If $$\frac{{{{\sin }^2}\theta - 3\sin \theta + 2}}{{{{\cos }^2}\theta }} = 1,$$     where 0°
  ক

  $$\frac{{2 + \sqrt 3 }}{3}$$

  খ

  $$\frac{{3 + 4\sqrt 3 }}{6}$$

  গ

  $$\frac{{9 + 4\sqrt 3 }}{6}$$

  ঘ

  $$\frac{{3 + 2\sqrt 3 }}{3}$$
• Evaluate the following expression in terms of trigonometric ratios.<br>$$\frac{{{{\cot }^2}A\left( {\sec A - 1} \right)}}{{1 + \sin A}}$$
  ক

  $$\frac{{{{\sec }^2}A\left( {1 + \sin A} \right)}}{{1 - \sec A}}$$

  খ

  $$\frac{{{{\sec }^2}A\left( {1 - \sin A} \right)}}{{1 + \sec A}}$$

  গ

  $$\frac{{{{\cot }^2}A\left( {1 + \sin A} \right)}}{{1 - \sec A}}$$

  ঘ

  $$\frac{{{{\cot }^2}A\left( {1 - \sin A} \right)}}{{1 - \sec A}}$$
• If 4 - 2sin²θ - 5cosθ = 0, 0°
  ক

  $$\frac{{3\sqrt 2 }}{2}$$

  খ

  $$\frac{{3\sqrt 3 }}{2}$$

  গ

  $$3\sqrt 2 $$

  ঘ

  $$2\sqrt 3 $$
• What is the value of cos15° - cos165°?
  ক

  $$\frac{{\sqrt 3 }}{{\sqrt 2 }}$$

  খ

  $$\frac{2}{{\sqrt 3 - 1}}$$

  গ

  $$\frac{{\sqrt 3 + 1}}{{\sqrt 2 }}$$

  ঘ

  $$\frac{{\sqrt 3 + 1}}{2}$$
• $$\frac{{\sin \theta - \cos \theta + 1}}{{\sin \theta + \cos \theta - 1}} = ?$$
  ক

  secθsinθ

  খ

  secθtanθ

  গ

  secθ + tanθ

  ঘ

  secθ - tanθ
• If cos53° = $$\frac{x}{y},$$ then sec53° + cot37° is equal to:
  ক

  $$\frac{{x + \sqrt {{y^2} - {x^2}} }}{y}$$

  খ

  $$\frac{{x + \sqrt {{y^2} - {x^2}} }}{x}$$

  গ

  $$\frac{{y + \sqrt {{y^2} - {x^2}} }}{x}$$

  ঘ

  $$\frac{{y + \sqrt {{y^2} - {x^2}} }}{y}$$
• If $$\frac{{1 + \sin \theta }}{{1 - \sin \theta }} = \frac{{{p^2}}}{{{q^2}}},$$    then secθ is equal to:
  ক

  $$\frac{{2{p^2}{q^2}}}{{{p^2} + {q^2}}}$$

  খ

  $$\frac{1}{2}\left( {\frac{q}{p} + \frac{p}{q}} \right)$$

  গ

  $$\frac{1}{{{p^2}}} + \frac{1}{{{q^2}}}$$

  ঘ

  $$\frac{{{p^2}{q^2}}}{{{p^2} + {q^2}}}$$
• $${\left( {\frac{{\sin \theta - 2{{\sin }^3}\theta }}{{2{{\cos }^3} - \cos \theta }}} \right)^2} + 1,$$     θ ≠ 45° is equal to:
  ক

  cosec²θ

  খ

  sec²θ

  গ

  cot²θ

  ঘ

  2tan²θ
• What is the value of $$\frac{{2\left( {1 - {{\sin }^2}\theta } \right){\text{cose}}{{\text{c}}^2}\theta }}{{{{\cot }^2}\theta \left( {1 + {{\tan }^2}\theta } \right)}} - 1$$
  ক

  sin2θ

  খ

  sin²θ

  গ

  cos²θ

  ঘ

  cos2θ
• If sinθ = 4cosθ, then what is the value of sinθcosθ?
  ক

  $$\frac{2}{9}$$

  খ

  $$\frac{3}{{10}}$$

  গ

  $$\frac{4}{{17}}$$

  ঘ

  $$\frac{3}{4}$$
• If 1 + 2tan²θ + 2sinθsec²θ = $$\frac{a}{b}$$, 0°
  ক

  secθ

  খ

  cosecθ

  গ

  cosθ

  ঘ

  sinθ
• The value of tan²θ + cot²θ - sec²θcosec²θ is equal to:
  ক

  -2

  খ

  1

  গ

  0

  ঘ

  -1
• If $$\frac{{\cos \left( {x + A} \right)}}{a} = \frac{{\cos \left( {x + 2A} \right)}}{b} = \frac{{\cos \left( {x + 3A} \right)}}{c}$$        and A = 60°, x = 15°, then the value of $${\left( {\frac{{a + c}}{b}} \right)^2} + {\left( {\frac{{a - c}}{b}} \right)^2}$$   is . . . . . . . .
  ক

  0

  খ

  4

  গ

  2

  ঘ

  1
• If tan40° = α, then find $$\frac{{\tan {{320}^ \circ } - \tan {{310}^ \circ }}}{{1 + \tan {{320}^ \circ } \cdot \tan {{310}^ \circ }}}$$
  ক

  $$\frac{{1 - {\alpha ^2}}}{\alpha }$$

  খ

  $$\frac{{1 + {\alpha ^2}}}{{2\alpha }}$$

  গ

  $$\frac{{1 - {\alpha ^2}}}{{2\alpha }}$$

  ঘ

  $$\frac{{1 + {\alpha ^2}}}{\alpha }$$
• What is the value of $$\frac{{1 + 2{{\cot }^2}\left( {{{90}^ \circ } - x} \right) - 2{\text{cosec}}\left( {{{90}^ \circ } - x} \right)\cot \left( {{{90}^ \circ } - x} \right)}}{{{\text{cosec}}\left( {{{90}^ \circ } - x} \right) - \cot \left( {{{90}^ \circ } - x} \right)}}?$$
  ক

  cosx + sinx

  খ

  sinx - cosx

  গ

  secx + tanx

  ঘ

  secx - tanx
• The value of $$\frac{{\sec \theta \left( {\sin \theta - 2{{\sin }^3}\theta } \right)}}{{2{{\cos }^3}\theta - \cos \theta }}$$    is:
  ক

  tanθ.cosθ

  খ

  secθ.sinθ

  গ

  secθ.tanθ

  ঘ

  sinθ.cosθ
• The value of $$\frac{{2{{\cos }^3}\theta - \cos \theta }}{{\sin \theta - 2{{\sin }^3}\theta }}:$$
  ক

  secθ

  খ

  sinθ

  গ

  cotθ

  ঘ

  tanθ
• If cos(A - B) = $$\frac{{\sqrt 3 }}{2}$$ and sec A = 2, 0° ≤ A ≤ 90°, 0° ≤ B ≤ 90° then what is the measure of B?
  ক

  60°

  খ

  0°

  গ

  30°

  ঘ

  90°
• $$\frac{{{{\left( {1 + \cos \theta } \right)}^2} + {{\sin }^2}\theta }}{{\left( {{\text{cose}}{{\text{c}}^2}\theta - 1} \right){{\sin }^2}\theta }} = ?$$
  ক

  cosθ(1 + sinθ)

  খ

  secθ(1 + sinθ)

  গ

  2cosθ(1 + secθ)

  ঘ

  2secθ(1 + secθ)