Class 10 – Introduction to Trigonometry – Important Questions

Important Questions Previous Years Questions

Introduction to Trigonometry – Important Questions

  1. If tan (A + B) = 1 and tan (A – B) = 1/√3 , 0° < A + B < 90° , A > B, then find the values of A and B.
  2. A, B and C are interior angles of a △ABC. Show that :-
    1. sin \frac{\textbf{B + C}}{\textbf{2}} = cos \frac{\textbf{A}}{\textbf{2}}
    2. If ∠A = 90°, then find the value of tan \frac{\textbf{B + C}}{\textbf{2}}.
  3. What is the value of (cos2 67° – sin2 23°) ?
  4. If 4 tan θ = 3, evaluate \frac{\textbf{4 sin}\theta - \textbf{cos}\theta + 1}{\textbf{4 sin}\theta + \textbf{cos}\theta - 1}.
  5. If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A.
  6. Prove that :
    \frac{\textbf{sin A - 2 sin}^{\textbf{3}}\textbf{A}}{\textbf{2 cos}^{\textbf{3}}\textbf{A} \textbf{ - cos A}} = tan A.
  7. Prove that:-
    \frac{\textbf{tan}^{\textbf{3}}\theta}{\textbf{1 + tan}^{\textbf{2}}\theta} + \frac{\textbf{cot}^{\textbf{3}}\theta}{\textbf{1 + cot}^{\textbf{2}}\theta} = sec θ cosec θ -2 sin θ cos θ.
  8. If 1 + sin2 θ = 3 sin θ cos θ, then prove that tan θ = 1 or tan θ = 1/2.
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