Question

Simplify:
1) sin^4 A + cos^4 A
2) sin^6 A + cos^6 A

Please answer quickly as I have an exam tomorrow ​

Answer 1

Answer:

We, have

LHS = sin

4

A + cos

4

A

⇒ LHS = (sin

2

A)

2

+(cos

2

A)

2

+2sin

2

Acos

2

A−2sin

2

Acos

2

A [Adding and subtracting 2 sin

2

A cos

2

A ]

⇒ LHS = (sin

2

A+cos

2

A)

2

−2sin

2

Acos

2

A=1−2sin

2

Acos

2

A=RHS

2.