Question

if 2 sin squared theta minus 5 sin theta + 4 equal to zero then find the value of sin theta + cos theta​

Answer 1

Answer:

Sinθ + Cosθ  = (1 ±√3) /2

Step-by-step explanation:

Correction in Question :

if 2 sin squared theta minus 5 sin theta + 2 equal to zero then find the value of sin theta + cos theta​

2Sin²θ - 5Sinθ + 2 = 0

=> 2Sin²θ - 4Sinθ - Sinθ + 2 = 0

=> 2Sinθ(Sinθ -2) -1(Sinθ -2) = 0

=> (Sinθ - 2)(2Sinθ - 1) = 0

=> Sinθ = 1/2   ( as Sinθ lies betwen -1 & 1)

Cos²θ = 1 - Sin²θ  

=> Cos²θ  = 1 - (1/2)²

=>  Cos²θ = 3/4

=> Cosθ = ±√3 /2

Sinθ + Cosθ  = 1/2 ±√3 /2

=> Sinθ + Cosθ  = (1 ±√3) /2