Question

I need help; how do I solve this question?

Solve the equation by first using a sum to product formula:
`sin4theta-sin2theta=cos3theta`

Answer 1

I may help you.

Explanation:

`sin4theta-sin2theta=cos3theta`

`=>2 cdot cos((4theta+2theta)/2)cdot sin((4theta-2theta)/2)=cos3theta`

`=>2cdot cos3theta cdot sintheta=cos3theta`

`=>2cos3theta sin theta-cos3theta=0`

`=>cos3theta cdot(2sintheta-1)=0`

Either,

`cos3theta=0=>cos3theta=cos(pi/2)=>3theta=2npi+- (pi/2)=>color(red)(ul(bar(|color(green)(theta=(2npi)/3+-(pi)/6)|`

or,

`2sintheta=1=>sintheta=1/2=>sintheta=sin(pi/6)=>color(red)(ul(bar(|color(green)(theta=npi+(-1)^n cdot (pi/6))|`

NOTE:-`" "color(red)(n in I`

Hope it helps...
Thank you...