1. Find the domain of the real-valued function f(x) =
A: For real-valued function: 4x − x2≥ 0
x2 − 4x ≤ 0
x(x − 4) ≤ 0
0 ≤ x ≤ 4
Domain : {x: x R, 0 ≤ x ≤ 4}.
2. If A is not an integral multiple of Π, Prove:
cosA. cos2A. cos4A. cos8A =
A: sin16A = 2 sin8A cos8A
= 2 (2 sin4A cos4A) cos8A
= 4(sin4A) cos4A cos8A
= 4(2 sin2A cos2A) cos4A cos8A
= 8(sin2A) cos2A cos4A cos8A
= 8(2 sinA cosA) cos2A cos4A cos8A
= 16(sinA) cosA cos2A cos4A cos8A
= cosA. cos2A. cos4A. cos8A
3. Solve : (sinx + cosx) = .
A:
4. Prove in ∆ABC :
cotA + cotB + cotC =
A:
5. Find the period of f(x) = sin (x + 2x +... + nx), n Z+, x R.
A:
6. Prove in ∆ ABC:
b cos2 + c. cos2 = s
A:
A:
Writer: Devi Prasad