Question

find the general solution of 4cos x - 3sec x=tan x............ Plz help

Answer 1

SOLUTION:--

4 cosx − 3 secx = tanx

4 cosx − 3/cosx = sinx/cosx

Multiply both sides by cosx

4 cos²x − 3 = sinx

4 (1−sin²x) − 3 = sinx

1 − 4 sin²x = sinx

4 sin²x + sinx − 1 = 0

sinx = (−1±√(1²−4*4*−1))/(2*4)

sinx = (−1±√17)/8

sinx = (√17−1)/8

x = sin⁻¹((√17−1)/8) + 2πn ≈ 2πn + 0.401053217

x = π−sin⁻¹((√17−1)/8) + 2πn ≈ 2πn + 2.740539437

sinx = −(√17+1)/8

x = −sin⁻¹((√17+1)/8) + 2πn ≈ 2πn − 0.695003598

x = π+sin⁻¹((√17+1)/8) + 2πn ≈ 2πn + 3.836596252

hope helped