Trigo, help pls: 2sin^2 (5x/2) + 4sin^2 (x/2)=3+cosx

[Nutella]

Hello guys! Help with trigonometry, maybe give formuls
2sin^2 (5x/2) + 4sin^2 (x/2)=3+cosx

 

[tkhunny]

Unclear what is wanted. Please show your best work,

 

[Deleted member 4993]

Hello guys! Help with trigonometry, maybe give formuls
2sin^2 (5x/2) + 4sin^2 (x/2)=3+cosx

sin(5x/2)

= sin(2x + x/2)

= sin(2x)* cos(x/2) + cos(2x)*sin(x/2)

= 2* sin(x)*cos(x)*cos(x/2) + [1 - 2sin^2(x)]*sin(x/2)

= 4* sin(x/2)*cos^2(x/2)*cos(x) + [1 - 2sin^2(x)]*sin(x/2)

Continue...

 

[mmm4444bot]

maybe give [formulae]

We could show you identities, to obtain results like the following, but would it help you to solve your equation?

cos(5*x) + 3*cos(x) = 0

OR

4*cos(x)^5 - 5*cos(x)^3 + 2*cos(x) = 0

We can solve your equation by inspection, using a combined graph of the left- and right-hand sides. :cool: