# Class 10 – Introduction to Trigonometry – Important 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 $\frac{\textbf{B&space;+&space;C}}{\textbf{2}}$ = 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 $\frac{\textbf{4&space;sin}\theta&space;-&space;\textbf{cos}\theta&space;+&space;1}{\textbf{4&space;sin}\theta&space;+&space;\textbf{cos}\theta&space;-&space;1}$.
5. If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A.
6. Prove that :
$\frac{\textbf{sin&space;A&space;-&space;2&space;sin}^{\textbf{3}}\textbf{A}}{\textbf{2&space;cos}^{\textbf{3}}\textbf{A}&space;\textbf{&space;-&space;cos&space;A}}$ = tan A.
7. Prove that:-
$\frac{\textbf{tan}^{\textbf{3}}\theta}{\textbf{1&space;+&space;tan}^{\textbf{2}}\theta}&space;+&space;\frac{\textbf{cot}^{\textbf{3}}\theta}{\textbf{1&space;+&space;cot}^{\textbf{2}}\theta}$ = 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.