Question

2 (sin⁶x + cos⁶x) -3(sin⁴x + cos⁴x)​

Answer 1

Answer:

Step-by-step explanation:

2 (sin⁶x + cos⁶x) -3(sin⁴x + cos⁴x)​

=> 2( (sin²x)³ + (cos²x)³) - 3((sin²x)² + (cos²x)²)

//a³ + b³ = (a+b)³ - 3ab(a+b) ; a² + b² = (a + b)² - 2ab

=> 2[ (sin²x+cos²x)³ - 3sin²xcos²x(sin²x+cos²x)] - 3 [(sin²x+cos²x)² -

    2sin²xcos²x]

//sin²x+cos²x = 1

=> 2[ 1 - 3sin²xcos²x] - 3[1 - 2sin²xcos²x]

=> 2 - 6sin²xcos²x - 3 + 6sin²xcos²x

=> 2 - 3

=> -1