Question

evaluate :
sin^6theta-cos^6theta​

Answer 1

Answer:

( sin²Ф - cos²Ф )( 1 - sinФcosФ )

Step-by-step explanation:

sin⁶Ф can be written as ( sin²Ф )³

cos⁶Ф can be written as ( cos²Ф)³

sin⁶Ф - cos⁶Ф

= ( sin²Ф )³ - ( cos²Ф )³

Use a³ - b³ = ( a - b )( a² + b² + ab )

= ( sin²Ф - cos²Ф )( sin⁴Ф + cos⁴Ф + sin²Фcos²Ф )

Use : a⁴ + b⁴ + a²b² = ( a² + b² )² - a²b²

= ( sin²Ф - cos²Ф )( ( sin²Ф + cos²Ф )² - sin  Ф cos Ф )

Use sin²Ф + cos²Ф = 1

= ( sin²Ф - cos²Ф )( 1 - sinФcosФ )