If 3θ is an acute angle, solve the following equations for θ:
(i) (cosec 3θ – 2) (cot 2θ – 1) = 0
(ii) (tan θ – 1) (cosec 3θ – 1) = 0
Answer :
(i) (cosec 3θ – 2) (cot 2θ – 1) = 0
cosec 3θ – 2 or cot 2θ – 1 = 0
⇒ cosec 3θ = 2 or cot 2θ = 1
So,
cosec 3θ = cosec 3θ° or cot 2θ =cot 45°
⇒ 3θ = 30° or 2θ = 45°
Thus,
θ = 30° or 45°.
(ii) (tan θ – 1) (cosec 3θ – 1) = 0
tan θ – 1 = 0 or cosec 3θ – 1 = 0
⇒ tan θ = 1 or cosec 3θ = 1
So,
tan θ = tan45° or cosec 3 θ = cosec 90°
⇒ θ = 45° or 3θ = 90° i.e. θ = 30°
Thus,
θ = 45° or 30°.
More Solutions: