If `xsina+ysin2a+zsin3a=sin4a` `xsinb+ysin2b+zsin3b=sin4b`, `xsinc+ysin2c+zsin3c=sin4c`, then the roots of the equation `t^3-(z/2)t^2-((y+2)/4)t+((z-x)/8)=0,a , b , c ,!=npi,` are (a)`sina ,sinb ,sinc` (b) `cosa ,cosb ,cosc` (c)`sin2a ,sin2b ,sin2c` (d) `cos2a ,cos2bcos2c`

Explanation

To solve the problem step by step, we will analyze the given equations and derive the roots of the polynomial.

### Step 1: Understanding the given equations
We have three equations:
1. \( x \sin a + y \sin 2a + z \sin 3a = \sin 4a \)
2. \( x \sin b + y \sin 2b + z \sin 3b = \sin 4b \)
3. \( x \sin c + y \sin 2c + z \sin 3c = \sin 4c \)

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