If 3sina + cosa = 0, then 1 / sin ^ 2A + cos ^ 2A = a.10/3 B.5 / 3 C.2 / 3 d. - 2

If 3sina + cosa = 0, then 1 / sin ^ 2A + cos ^ 2A = a.10/3 B.5 / 3 C.2 / 3 d. - 2

3sinA+cosA = 0
tanA = -1/3
(sinA)^2 = 1/10
(cosA)^2 = 9/10
1/(sinA)^2 + (cosA)^2
= 10+9/10
=109/10

Given √ 3sina / 2 + [sin (a - π / 2)] / [cos (π + A / 2)] * cosa / 2 = 1, a belongs to (0,2 π), find the value of A

3sin(a/2)＋[sin(a-π/2)]／[cos(π＋a/2)]*cos(a/2)＝√3sin(a/2)＋[-cosa]／[-cos(a/2)]*cos(a/2)＝√3sin(a/2)＋cosa＝1.
If cosa = 1-2 [sin (A / 2)] ^ 2, then √ 3sin (A / 2) - 2 [sin (A / 2)] ^ 2 = 0, so sin (A / 2) = 0 or √ 3 / 2
A ∈ (0,2 π), then a / 2 ∈ (0, π), so sin (A / 2) = 0 has no solution, the solution of sin (A / 2) = 3 / 2 is a / 2 = π / 3 or 2 π / 3, that is, a = 2 π / 3 or 4 π / 3
So, a = 2 π / 3 or 4 π / 3