Question

cos²a-3 cosa+2=sin²a​

Answer 1

Answer:

Cos2a-3cosA+2/sin2a= 1

[(Sin2a*cos2a)-(3cosA*sin2A)+2]/sin2A=1

(1+2+3cosA*sin2A)/sin2A=1

(3+3cosA-sin2A)/sin2A=1

sin2A/sin2A=1

1=1

Answer 2

Step-by-step explanation:

=> Cos²a - 3 cos a + 2 = sin²a

=> Cos²a - 3 cos a + 2 - sin²a = 0

we know that, sin²a + Cos²a = 1

sin²a = 1 - Cos²a

=> Cos²a - 3 cos a + 2 - ( 1 - Cos²a) = 0

=> 2Cos²a - 3 cos a + 1 = 0

=> 2Cos²a - 2 cos a - Cos a + 1 = 0

=> 2 Cos a ( Cos a - 1) -1 ( Cos a - 1) = 0

=> (2 Cos a - 1) ( Cos a - 1) = 0

=> 2 Cos a - 1 = 0 or, Cos a - 1 =0

=> Cos a = 1/2 or, Cos a = 1

thus, Cos a = 60° or Cos a = 0°