1. cos3x=2sin (3π/2-x)

2. cosx-sin11x=o

3. sinx+sin7x-cos5s-cos (π-3x) = o

1

cos3x=-2cosx

4cos³x-3cosx+2cosx=0

4cos³x-cosx=0

cosx (4cos²x-1) = 0

cosx=0⇒x=π/2+πn, n∈z

4cos²x-1=0

4 (1+cos2x) / 2=1

1+cos2x=1/2

cos2x=-1/2

2x=+-2π/3+2πk

x=+-π/3+πk, k∈z

2

cosx-cos (π/2-11x) = 0

-2sin (6x-π/4) sin (-5x+π/4) = 0

2sin (6x-π/4) sin (5x-π/4) = 0

sin (6x-π/4) = 0

6x-π/4=πn

6x=π/4+πn

x=π/24+πn/6, n∈z

sin (5x-π/4) = 0

5x-π/4=πk

5x=π/4+πk

x=π/20+πk/5, k∈z

3

(sinx+sin7x) + (cos3x-cos5x) = 0

2sin4xcos3x+2sin4xsinx=0

2sin4x * (cos3x+sinx) = 0

sin4x=0

4x=πn

x=πn/4

cos3x+cos (π/2-x) = 0

2cos (x+π/4) cos (2x-π/4) = 0

cos (x+π/4) = 0

x+π/4=π/2+πk

x=π/4+πk, k∈z

cos (2x-π/4) = 0

2x-π/4=π/2+πm

2x=3π/4+πm

x=3π/8+πm/2, m∈z