NTA Abhyas JEE Main2020MathematicsTrigonometric EquationsPractice
The set of all values of a for which the equation cos ⁡ 2 x + a sin ⁡ x = 2 a - 7 has a solution is
Options
- A( - ∞ , 2 )
- B[ 2,6 ]
- C( 6 , ∞ )
- D( - ∞ , ∞ )
Correct answer
B. [ 2,6 ]
Step-by-step solution
cos ⁡ 2 x + a sin ⁡ x = 2 a - 7 i.e. 2 sin 2 ⁡ x - a sin ⁡ x + 2 a - 8 = 0 sin ⁡ x = a ± a 2 - 8 2 a - 8 4 = a ± a - 8 4 sin ⁡ x = a - 4 2   or   2 Hence, - 1 ≤ a - 4 2 ≤ 1 The range of a is [ 2,6 ]