Question

The value of cos 60°. cos 30° - sin 60°. sin 30°=​

Answer 1

Answer:

You can do each calculation separately and do all the math, or you can recognize the angle difference formula for cosine:

cos

(

A

−

B

)

=

cos

A

×

cos

B

+

sin

A

×

sin

B

In this case,

A

is

60

∘

and

B

is

30

∘

. Use the formula backward now:

=

cos

60

∘

×

cos

30

∘

+

sin

60

∘

×

sin

30

∘

=

cos

(

60

∘

−

30

∘

)

=

cos

(

30

∘

)

=

√

3

2

We can verify our answer by doing all the calculations:

=

cos

60

∘

×

cos

30

∘

+

sin

60

∘

×

sin

30

∘

=

1

2

×

√

3

2

+

√

3

2

×

1

2

=

√

3

4

+

√

3

4

=

2

√

3

4

=

√

3

2