Double angle identities help

Question

5 Sin 2x - 6 sin x = 0

 

Sin 2x = cos x

 

Cos 2x + 5 = 4 sin x

Answer 1

sin(2x) = 2 sin(x)cos(x)

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

 

5 sin(2x) - 6 sin(x) = 0

 

5 (2 sin(x)cos(x)) - 6 sin(x) = 0

 

(2 sin(x))(5 cos(x) – 3) = 0

 

By Zero Product Property:

 

sin(x) = 0 ==> two points on Unit Circle

x = n pi, n integer

 

or

 

5 cos(x) – 3 = 0

cos(x) = 3/5 = 0.6 ==> two points on Unit Circle

x ≈ (2n ± 0.29516723530087) pi, n integer

 

Try to do the rest, Richard.