Question

using the formula cos A =+- root over( 1+cos 2A)/2 find the value of 67 1/2 degree​

Answer 1

Answer:

formula doesn't tell us whether

sin

67.5

∘

is positive or negative, but, since it is an acute angle we know that the sine is positive. (Be careful of the difference between "sign" and "sine").

We also need

cos

135

∘

. (That is the special angle that is

45

∘

in Quadrant II.)

cos

135

∘

=

−

√

2

2

.

Now use the formula ans simplify:

sin

67.5

∘

=

sin

(

1

2

(

135

∘

)

)

=

√

1

−

cos

135

∘

2

=







⎷

1

−

(

−

√

2

2

)

2

=







⎷

1

+

√

2

2

2

=

√

2

+

√

2

4

=

√

2

+

√

2

2

sin

67.5

∘

=

√

2

+

√

2

2