Question

EVALUATE :- sin^6 A - cos^6 A

Answer 1

HELLO DEAR,


we know that:-

a³ – b³ = (a – b) (a² + ab + b² ).---------(1)

a⁴+b⁴ = (a²+b²)² - 2a²b²--------(2)

(sin²A+cos²A)=1-----(3)

sin^6 A - cos^6 A


=> (sin²A)³ -(cos²A)³-------using(1)


=> (sin²A-cos²A)[(SIN ⁴A+COS⁴A)+SIN²A COS²A]


=>(sin²A-cos²A[(sin²A+cos²A)²-2sin²Acos²A+sin²Acos²A]
-------------using (2)

=> (sin²A-cos²A)[(1)²-sin²Acos²A]-------------using (3)


=> (sin²A-cos²A)[1-sin²Acos²A]



I HOPE ITS HELP YOU DEAR,
THANKS