Question

Solve 4cosx - 3secx = tanx

Answer 1

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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

Answer 2

Answer:

firstly convert sec x and tan x into sin and cos then covert cos^2x in 1_sin^2x and make quadratic equation then solve it and use sinx=siny