Example 8 - Chapter 8 Class 10 Introduction to Trignometry

Transcript

Example 8 If sin (A – B) = 1/2 , cos (A + B) = 1/2 , 0° ∠ A + ∠ B ≤ 90° , A > B, find A and B. Given data, sin (A – B) = 𝟏/𝟐 But we know that sin 30° = 1/2 Thus, sin (A – B) = sin 30° A – B = 30° cos (A + B) = 𝟏/𝟐 But we know that cos 60° = 1/2 Thus cos (A + B) = cos 60° A + B = 60° Our equations are A − B = 30° …(1) A + B = 60° …(2) Adding (1) and (2) A – B + A + B = 60° + 30° 2A = 90° A = (90°)/2 A = 45° Putting A = "45°" in (2) A + B = 60° 45° + B = 60° B = 60° − 45° B = 15° Hence, A = 45° , B = 15°