NTA Abhyas JEE Main2020MathematicsTrigonometric EquationsPractice
If sin 2 A = 1 2 and sin 2 B = - 1 2 , then which of the following is false?
Options
- Asin A + B may be 0
- Bcos A - B may be 0
- Csin A + B or cos A - B is zero
- Dsin A + B = 0
Correct answer
D. sin A + B = 0
Step-by-step solution
sin ⁡ 2 A = 1 2 , sin ⁡ 2 B = - 1 2 ⇒ sin ⁡ 2 A + sin ⁡ 2 B = 0 ⇒ 2 sin ⁡ A + B cos ⁡ A - B = 0 ⇒ sin ⁡ A + B = 0 or cos ⁡ A - B = 0 Hence, 4 th option is false.