Question

Find

the general solution of the equation .
2sinx + √3cosx = 1+ sinx​

Answer 1

Answer:

x = (2n+1)π + π/6

Step-by-step explanation:

2sinx + √3cosx = 1+ sinx

sinx + √3cosx = 1

r cosy =1 ; r siny = √3

r^2 = (√3)^2 + 1^2

r = 2

sin y = 1/2 : cos y = √3/2

hence...y = 30° = π/6

now...2 cos π/6 sinx + 2 sin π/6cosx = 1

i,e..sin 2sin (π+x) = 1

means...sin (π+x) =1/2

sin (π+x) = sin 30° = sin π/6

π + x = π/6

x = -5π/6

x = -π + π/6 = π + π/6

x = (2n+1)π + π/6