If x = log e cot π 4 + θ and θ ∈ - π 4 , π 4 , then consider the following statements: I : cosh x = sec 2 θ II : sinh x = - tan 2 θ Then which one of the following options is true?

Step-by-step solution

Given, x = log e cot π 4 + θ ⇒ e x = cot π 4 + θ = cos θ - sin θ cos θ + sin θ Now, cos h x = e x + e - x 2 = e x + 1 e x 2 = 1 2 cos θ - sin θ cos θ + sin θ + cos θ + sin θ cos θ - sin θ = 1 2 cos θ - sin θ 2 + cos θ + sin θ 2 cos θ + sin θ cos θ - sin θ = 1 2 2 cos 2 θ - sin 2 θ = 1 cos 2 θ = sec 2 θ And, sin h x = e x - e - x 2 = e x - 1 e x 2 = 1 2 cos θ - sin &#