Solve 3sinx 4cosx 2 Exact solutions are not possible for t

Solve 3sinx + 4cosx = 2. Exact solutions are not possible for this problem. To complete the solution, you will need to use a calculator. Use radian mode.

Solution

3sin x + 4cos x = 2

3 sin x = 2 - 4 cos x

(3sin x )^2 = ( 2- 4 cos x )^2

9 sin^2 x - ( 2 - 4 cos x )^2 = 0

sin^2 x = ( 1- cos^2 x )

on simplifying we get

5 + 16cos x - 25cos^2 x = 0

cos x = 1/25 ( 8 - 3 sqrt 21)

cos x = 1/25 ( 8 + 3 sqrt 21)

for, cos x = 1/25 ( 8 - 3 sqrt 21)

x = 2pi*n - arccos(1/25 ( 8 - 3 sqrt 21) ) , 2pi*n + arccos(1/25 ( 8 - 3 sqrt 21) )

cos x = 1/25 ( 8 + 3 sqrt 21)

x = 2pi*n - arccos(1/25 ( 8 + 3 sqrt 21) ) , 2pi*n + arccos(1/25 ( 8 + 3 sqrt 21) )