Question

Solve for A .
2sin²2A + sin2A -1 = 0 ​

Answer 1

Answer:

2 sin²2A + sin2A - 1 = 0

⇒ 2 sin²2A + 2 sin2A - sin2A - 1 = 0

⇒ 2 sin2A ( sin2A + 1 ) - 1 (sin2A + 1) = 0

⇒ ( 2sin2A - 1 )( sin2A + 1) = 0

sin2A = 1/2

⇒ 2A = 30° or 150° .

A = 15° or 75°.

sin 2A = -1

A = 135°.

If you want general solution then :

A = nπ + (-1)^n π/12 ,

A = nπ + (-1)^n 5π/12 .

A = (4n + 3)π/2