Question

2(cos^6+sin^6)-3(cos^4+sin^4)

Answer 1

ans is 1
2cos^6+2sin^6-3cos^4-4sin^4
-cos^2-sin^2    [sin^2+cos^2 = 1]=[-1=-sin^2-cos^2]
so sin^2+cos^2=1
 so ans is 1
 

Answer 2

2(cos^6+sin^6)-3(cos^4+sin^4)
2[(cos²)³ +(sin²)³] -3[(cos²)² +(sin²)²]
on using formula a³+b³=(a+b)(a²+b²-ab)
2[(cos²+sin²)(cos^4+sin^4-cos²sin²)] -3[cos^4+sin^4]
using sin²x+cos²x=1
2[cos^4+sin^4-sin²cos²] -3cos^4-3sin^4
-cos^4-sin^4-2sin²cos²
-[(cos²)² +(sin²)² +2sin²cos²]
-[(sin²+cos²)²]
-1 is answer