Solve the following trignometrical equations for 0 less than equals to x less than equals to 360 : (i) 6cos^2x+7sinx-8=0, (ii) 6 sin^2 x+5cosx-7=0, (iii) tan^2 x-5tanx+6=0,

Answer 1

(i) 6sin²x - 7sinx + 2 = 0; (2sinx - 1)(3sinx - 2) = 0; sinx = 1/2; x = π/6 or x = 5π/6

sinx = 2/3; x = sin^-1(2/3) or x = π - sin^-1(2/3)

(ii) 6cos²x - 5cosx + 1 = 0; (2cos - 1)(3cosx - 1) = 0;;

cosx = 1/2, x = π/3 or x = 5π/3;

cosx= 1/3; x = cos^-1(1/3) or x = 2π - cos^-1(2/3)