1. Solve the following equations for A, if :
(i) 2 sin A = 1
(ii) 2 cos 2 A = 1
(iii) sin 3 A =
(iv) sec 2 A = 2
(v) V3 tan A = 1
(vi) tan 3 A = 1
(vii) 2 sin 3 A = 1
(viii) V3 cot 2 A = 1
Answers
(i) Solution :
=> 2sinA = 1
=> sinA = 1/2
=> sinA = sin30°
=> A = 30°
(ii) Solution :
=> 2cos2A = 1
=> cos2A = 1/2
=> cos2A = cos60°
=> 2A = 60°
=> A = 60°/2
=> A = 30°
(iii) Solution :
=> sin3A = 1
=> sin3A = sin90°
=> 3A = 90°
=> A = 90°/3
=> A = 30°
(iv) Solution :
=> sec2A = 2
=> sec2A = sec60°
=> 2A = 60°
=> A = 60°/2
=> A = 30°
(v) Solution :
=> √3tanA = 1
=> tanA = 1/√3
=> tanA = tan30°
=> A = 30°
(vi) Solution :
=> tan3A = 1
=> tan3A = tan45°
=> 3A = 45°
=> A = 45°/3
=> A = 15°
(vii) Solution :
=> 2sin3A = 1
=> sin3A = 1/2
=> sin3A = sin30°
=> 3A = 30°
=> A = 30°/3
=> A = 10°
(viii) Solution :
=> √3cot2A = 1
=> cot2A = 1/√3
=> cot2A = cot60°
=> 2A = 60°
=> A = 60°/2
=> A = 30°
Answer:
(i) Solution :
=> 2sinA = 1
=> sinA = 1/2
=> sinA = sin30°
=> A = 30°
(ii) Solution :
=> 2cos2A = 1
=> cos2A = 1/2
=> cos2A = cos60°
=> 2A = 60°
=> A = 60°/2
=> A = 30°
(iii) Solution :
=> sin3A = 1
=> sin3A = sin90°
=> 3A = 90°
=> A = 90°/3
=> A = 30°
(iv) Solution :
=> sec2A = 2
=> sec2A = sec60°
=> 2A = 60°
=> A = 60°/2
=> A = 30°
(v) Solution :
=> √3tanA = 1
=> tanA = 1/√3
=> tanA = tan30°
=> A = 30°
(vi) Solution :
=> tan3A = 1
=> tan3A = tan45°
=> 3A = 45°
=> A = 45°/3
=> A = 15°
(vii) Solution :
=> 2sin3A = 1
=> sin3A = 1/2
=> sin3A = sin30°
=> 3A = 30°
=> A = 30°/3
=> A = 10°
(viii) Solution :
=> √3cot2A = 1
=> cot2A = 1/√3
=> cot2A = cot60°
=> 2A = 60°
=> A = 60°/2
=> A = 30°