Q 5f no 6
If Sin Ø + Sin 2Ø = a, & Cos Ø + Cos 2Ø = b Prove that (a^{2 }+ b^{2}) (a^{2 }+ b^{2}3) =2 b
 
Sin Ø + Sin 2Ø = a Let c = Ø+2Ø = 3Ø and d = Ø2Ø = Ø c + d = 2Ø c  d = 4Ø
Therefore a = 2 Sin Ø. Cos 2Ø & a^{2 }= 4 Sin^{2} Ø. Cos^{2}2 Ø  Cos Ø + Cos 2Ø = b Let c = Ø+2Ø = 3Ø and d = Ø2Ø = Ø c + d = 2Ø c  d = 4Ø
Therefore b = 2 Cos Ø. Cos 2Ø & b^{2 }= 4 Cos^{2} Ø. Cos^{2}2 Ø

a^{2 }+ b^{2} = 4 Sin^{2} Ø. Cos^{2}2 Ø + 4 Cos^{2} Ø. Cos^{2}2 Ø = 4 Cos^{2}2 Ø (Sin^{2 }Ø + Cos^{2} Ø) = 4 Cos^{2}2 Ø  
Therefore (a^{2 }+ b^{2}) (a^{2 }+ b^{2}3) = 4 Cos^{2}2Ø (4 Cos^{2}2 Ø3) = 16 Cos^{4 }2Ø – 12 Cos^{2 }2Ø =4 Cos2Ø (4Cos^{3}2Ø – 3Cos 2Ø) =4 Cos 2Ø. Cos 6Ø
 
2b = 4 Cos Ø. Cos 2Ø  
Conclusion: 4 Cos Ø. Cos 2Ø = 4 Cos 2Ø. Cos 6Ø
CosØ = Cos 6Ø (??????)
