AP EAMCET202119 Aug 2021Evening ShiftMathematicsTrigonometric EquationsActual
If f ( x ) = cot x 1 + cot x and α + β = 5 π 4 then the value of f ( α ) f ( β ) =
Options
- A3 2
- B− 3 2
- C− 1 2
- D1 2
Correct answer
D. 1 2
Step-by-step solution
Given, f ( x ) = cot x 1 + cot x and α + β = 5 π 4 ⇒ cot α + β = cot 5 π 4 ⇒ cotαcotβ - 1 cotβ + cotα = 1 ⇒ cotαcotβ = 1 + cotβ + cotα Now, f α = cotα 1 + cot α ,   f β = cotβ 1 + cotβ Then, f α f β = cotα 1 + cot α × cotβ 1 + cotβ = cotαcotβ 1 + cotαcotβ + cot α + cotβ = cotαcotβ 2 cotαcotβ = 1 2