Ex 8.2, 2 (iii) (MCQ) - Chapter 8 Class 10 Introduction to Trignometry

Transcript

Ex 8.2, 2 Choose the correct option and justify your choice : (iii) sin 2A = 2 sin A is true when A = 0° (B) 30° (C) 45° (D) 60° Given sin 2A = 2 sin A Here, we substitute the value of option in the equation and whichever satisfies the question would be solution . Checking option (A) - A = 0° Now, sin 2A = 2sin A sin 2(0) = 2 sin(0) sin 0° = 2 sin 0° 0 = 0 L.H.S = R.H.S Hence, Option A is correct Checking option (B) - A = 30° sin 2A = 2 sin A sin 2(30°) = 2(sin 30°) sin 60° = 2 sin 30° √3/2=2 × 1/2 √3/2=1 But √𝟑/𝟐 " ≠ " 𝟏 So, Option (B) is not possible Checking option (C) - A = 45° sin 2A = 2 sin A sin 2(45°) = 2 sin 45° sin 90° = 2 sin45° 1 = 2 ×1/√2 1 = √2 × √2 ×1/√2 1 = √2 But 1 ≠√𝟐 So, Option (C) is not possible Checking option (D) - A = 60° sin 2A = 2 sin A sin 2(60°) = 2 sin(60°) sin 120° = 2 sin 60° sin (90 + 30) = 2 sin 60° cos 30° = 2sin 60° √3/2=2×√3/2 √3/2=√3 But √𝟑/𝟐≠√𝟑 So, Option (D) is not possible So, the correct answer is (a)