Question

Evaluate....

sin^4A + 2sin^2A(1 - 1/cosec^2A) + cos^4A​

Answer 1

Answer:

Our starting goal is to turn all terms into cosine. Use the identity

sin

2

θ

+

cos

2

θ

=

1

.

sin

a

+

1

−

cos

2

a

=

1

sin

a

−

cos

2

a

=

0

sin

a

=

cos

2

a

Square both sides to get rid of the sine.

(

sin

a

)

2

=

(

cos

2

a

)

2

sin

2

a

=

cos

4

a

Reuse

sin

2

θ

+

cos

2

θ

=

1

:

1

−

cos

2

a

=

cos

4

a

1

=

cos

4

a

+

cos

2

a

Hopefully this helps!