JEE Main2014MathematicsTrigonometric Ratios & IdentitiesActual
Let f k x = 1 k sin k x + cos k x where x ∈ R and k ≥1 . Then f 4 x - f 6 x equals
Options
- A1 4
- B1 1 2
- C1 6
- D1 3
Correct answer
B. 1 1 2
Step-by-step solution
f 4 x = 1 4 sin 4 x + cos 4 x = 1 4 sin 2 x + cos 2 x 2 - 2 sin 2 x   cos 2 x = 1 4 1 - 2 sin 2 x   cos 2 x f 6 x = 1 6 sin 6 x + cos 6 x = 1 6 sin 2 x + cos 2 x 3 - 3 sin 2 x   cos 2 x sin 2 x + cos 2 x = 1 6 1 - 3 sin 2 x   cos 2 x 1 f 4 x - f 6 x = 1 4 - 1 6 = 1 1 2