Question

Find the value of cos^2 15 exactly

Answer 1

\[\cos^2 15\]
That?

Answer 2

yea

Answer 3

Let A = 15
cos A = cos 15
cos (2A) = cos (2x15) = cos 30.

Do you know what cos 30 is?

Answer 4

sqrt(3)/2

Answer 5

then what??...

Answer 6

Use the identity:
\[cos2A = 2cos^2A -1\]to get \(cos^2A\)

Answer 7

so is the answer sqrt(3) + 2?

Answer 8

Maybe you'd like to check your calculations again.

Answer 9

ok can you do it for me?

Answer 10

No, but I don't mind checking it for you.

Answer 11

ok

Answer 12

so you go:\[\frac{ \sqrt{3} }{ 2 } + 1 = 2 \cos^2 \]

Answer 13

then\[\frac{ (\frac{ \sqrt{3} }{ 2 } + 1) }{ 2 } = \cos^2 A\]

Answer 14

then what after that?

Answer 15

Almost there.
Simplify \(\frac{ (\frac{ \sqrt{3} }{ 2 } + 1) }{ 2 }\)

Answer 16

so sqrt(3) + 1?

Answer 17

No.

Answer 18

sqrt(3) + 2?

Answer 19

No...

Answer 20

then how

Answer 21

\[\frac{ (\frac{ \sqrt{3} }{ 2 } + 1) }{ 2 } = (\frac{ \sqrt{3} }{ 2\times2 } + \frac{1}{2}) \]You may want to further simplify it.