4sin^2a+3sin2a=4 cos^2a, найти sin2a при п/2

4 sin²a + 3 sin2a = 4 cos²a,

4 * (cos²a - sin²a) = 3 sin2a,

4 cos2a - 3 sin2a = 0,

4 cos2a/cos2a - 3 sin2a/cos2a = 0/cos2a,

4 - 3 tg 2a = 0,

tg 2a = 4/3, выведем отсюда сtg 2a:

сtg 2a = 3/4,

sin2a + соs2a = 1,

sin²2a/sin²2a + соs²2a/sin²2a = 1/sin²2a,

1 + сtg ²2a = 1/sin²2a,

sin²2a = 1 / (1 + сtg ²2a),

sin²2a = 1 / (1 + 9/16),

sin²2a = 1 / (25/16),

sin²2a = 16/25,

sin2a = 4/5.