2sin 6cos6 - 3sin4cos41 0ans sin23

Question

2(sin ⁶?+cos⁶?) - 3(sin⁴?+cos⁴?)+1 = 0

Ans:    (Sin²?)3  + (Cos²?)3-3 (Sin⁴?+(Cos⁴?)+1=0

Consider (Sin²?)3  +(Cos²?)3

⇒(Sin²?+Cos²?)3-3 Sin²?Cos²?( Sin²?+Cos²?)

= 1- 3Sin²? Cos²?

Sin⁴?+Cos⁴?(Sin²?)2+(Cos²?)2

= (Sin²?+Cos²?)2-2 Sin²? Cos²?

= 1- 2 Sin²? Cos²?

= 2(Sin⁶?+Cos⁶?)-3(Sin⁴?+Cos⁴?) +1

= 2 (1-3 Sin²? Cos²?)-3 (1-2 Sin²?+Cos²?)+1