Problem 1 Problem 2SolutionProblem 1 Mx Cosecx Sinx Cosx

Problem #1

Problem #2

Solution

Problem # 1

M(x) = Cosec(x) - Sin(x) + Cos(x)Cot(x) = 0

I/Sin(x) - Sin(x) + Cos(x).Cos(x) / Sin(x) = 0

(1 - Sin²(x)) / Sin(x) + Cos²(x) / Sin(x) = 0

Simplifying we get,

1 - Sin²(x) + Cos²(x) = 0
Substituting 1 as Sin²(x) + Cos²(x), we get
SIn²(x) + Cos²(x) - Sin²(x) + Cos² (x) = 0
2Cos²(x) = 0; Cos²(x) = 0

Since Cos 180⁰ = 0; x = Pi

Poblem # 2

J(x) = Sqrt (x ²+1) / 2x = 1

Sqrt (x ²+1) = 2x
Suaring both sides we get,

x² + 1 = 4x²
Simplying we get,
3x² = 1
x² = 1/3
x = 1 / sqrt(3)