Question

4cosx cos (x+pi/3)+cos^2 (pi-2pi/3)=cos3x​

Answer 1

Answer:

Explanation:

=4cosx*cos(60-x)*cos(60+x)

=4cosx*(cos60*cosx+sin60*sinx)* (cos60*cosx-sin60*sinx)

= 4cosx*(cosx/2 + 3½sinx/2)*(cosx/2 - 3½sinx/2)

= 4cosx*(cos²x/4 - 3sin²x/4)

= 4cosx*(cos²x - 3sin²x)/4

= cosx (cos²x - 3sin²x)

= cosx (cos²x - 3(1-cos²x))

= cosx (cos²x - 3 + 3cos²x)

= cosx (4cos²x - 3)

= 4cos³x - 3cosx

चूँकि ,( cos3x = 4cos³x - 3cosx)

= cos3x (hence proof)