Question

sin6 + cos6 = 1− 3sin2 cos2​

Answer 1

Answer:

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Answer 2

Answer:

Just to help simplify things let

S

=

sin

2

x

Using the fundamental identity

sin

2

A

+

cos

2

A

≡

1

we have;

S

+

cos

2

x

=

1

⇒

cos

2

x

=

1

−

S

So we can then write the initial equation:

sin

6

x

+

cos

6

x

=

1

−

3

sin

2

x

cos

2

as:

S

3

+

(

1

−

S

)

3

=

1

−

3

S

(

1

−

S

)

∴

S

3

+

1

−

3

S

+

3

S

2

−

S

3

=

1

−

3

S

+

3

S

2

∴

0

=

0