Question

Class X
Maths

Solve (cos squared theta minus 3 cos theta + 2) / sin square theta = 1.

With steps.

Answer 1

Answer:

θ = 60°,0°

Step-by-step explanation:

Given Equation is (cos²θ - 3cosθ + 2)/sin²θ = 1

⇒ cos²θ - 3cosθ + 2 = sin²θ

⇒ cos²θ - 3cosθ + 2 = (1 - cos²θ)

⇒ cos²θ - 3cosθ + 2 - 1 + cos²θ = 0

⇒ 2cos²θ - 3cosθ + 1 = 0

⇒ 2cos²θ - 2cosθ - cosθ + 1 = 0

⇒ 2cosθ(cosθ - 1) - (cosθ - 1) = 0

⇒ (2cosθ - 1)(cosθ - 1) = 0

⇒ cosθ = (1/2) (or) cosθ = 1

⇒ θ = 60° (or) 0°

Hope it helps!

Answer 2

Step-by-step explanation:

cosA^2-3cosA+2 =1(sinA^2) so add two cosA ^2 on both sides then 3(cosA^2)-3cosA+2 =1 hence cosA=0 or 60 therefore A=60 degrees or 0 degrees