Class 10 – Introduction to Trigonometry – Important Questions

Introduction to Trigonometry – Important Questions

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.
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 $\frac{\textbf{B + C}}{\textbf{2}}$ .
What is the value of (cos² 67° – sin² 23°) ?
If 4 tan θ = 3, evaluate $\frac{\textbf{4 sin}\theta - \textbf{cos}\theta + 1}{\textbf{4 sin}\theta + \textbf{cos}\theta - 1}$ .
If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A.
Prove that :
$\frac{\textbf{sin A - 2 sin}^{\textbf{3}}\textbf{A}}{\textbf{2 cos}^{\textbf{3}}\textbf{A} \textbf{ - cos A}}$ = tan A.
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.
If 1 + sin² θ = 3 sin θ cos θ, then prove that tan θ = 1 or tan θ = 1/2.

Class 10