Question

Question 6 Find the general solution of the equation cos 3x + cos x - cos 2x = 0

Class X1 - Maths -Trigonometric Functions Page 78

Answer 1

cos3x + cosx - cos2x =0
=>(cos3x + cosx) - cos2x = 0
use the formula,
cosC + cosD = 2cos(C+D)/2.cos(C-D)/2

=>{2cos(3x + x)/2.cos(3x-x)/2}-cos2x =0
=>{2cos2x.cosx } - cos2x = 0
=> cos2x(2cosx - 1) = 0
here, cosx = 1/2 or cos2x = 0

cos2x = 0
Then, 2x = (2n+1)π/2
x = (2n+1)π/4

again,
cosx = 1/2
cosx = cos(π/3)
x = 2nπ ± (π/3)

Hence, the solutions are
x = (2n+1)π/4 or 2nπ ± (π/3)