Question

Solve without using a calculator: sin²20° + sec²20°

Answer 1

Step-by-step explanation:

sin

2

(

20

°

)

+

sec

2

(

20

°

)

Simplify each term.

Tap for fewer steps...

Rewrite

sec

(

20

°

)

in terms of sines and cosines.

sin

2

(

20

°

)

+

(

1

cos

(

20

°

)

)

2

Apply the product rule to

1

cos

(

20

°

)

.

sin

2

(

20

°

)

+

1

2

cos

2

(

20

°

)

One to any power is one.

sin

2

(

20

°

)

+

1

cos

2

(

20

°

)

Simplify each term.

Tap for fewer steps...

Rewrite

1

as

1

2

.

sin

2

(

20

°

)

+

1

2

cos

2

(

20

°

)

Rewrite

1

2

cos

2

(

20

°

)

as

(

1

cos

(

20

°

)

)

2

.

sin

2

(

20

°

)

+

(

1

cos

(

20

°

)

)

2

Convert from

1

cos

(

20

°

)

to

sec

(

20

°

)

.

sin

2

(

20

°

)

+

sec

2

(

20

°

)

The result can be shown in multiple forms.

Exact Form:

sin

2

(

20

°

)

+

sec

2

(

20

°

)

Decimal Form:

1.24945210