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

Question

Let f k x = 1 k sin k &#160; x + cos k &#160; x where x &#8712; R and k &#8805;1 . Then f 4 x - f 6 x equals

Aicharya · Accepted Answer

f 4 x = 1 4 sin 4 x + cos 4 x = 1 4 sin 2 x + cos 2 x 2 - 2 sin 2 x &#160; cos 2 x = 1 4 1 - 2 sin 2 x &#160; 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 &#160; cos 2 x sin 2 x + cos 2 x = 1 6 1 - 3 sin 2 x &#160; cos 2 x 1 f 4 x - f 6 x = 1 4 - 1 6 = 1 1 2

Let f k x = 1 k sin k &#160; x + cos k &#160; x where x &#8712; R and k &#8805;1 . Then f 4 x - f 6 x equals

Solution

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