Question

Simplify
sin^2(54)+cos^2(72)

Answer 1

Please don't just go sin 54 = blah and cos(72) = blah, so blah + blah = blahblah

Answer 2

@Callisto

Answer 3

is 54 the actual number or is that in 54 degrees?

Answer 4

54 degrees

Answer 5

So you just want to know how to computte this by hand?

Answer 6

yes

Answer 7

why did you go into radians?

Answer 8

so what is x equal to?

Answer 9

I fluttered that up ignore me.

Answer 10

Hopefully zrocker can help you X_X

Answer 11

\[sin^2(54)+cos^2(72)\]\[=(cos(90-54))^2+cos^2(72)\]\[=cos^2(36)+cos^2(72)\]
That looks nicer

Answer 12

Oh, wait... let me try now

Answer 13

Okay :|

Answer 14

cos^2(36) + (2cos^2(36)-1)^2

Answer 15

am i right?

Answer 16

Yes.

Answer 17

now... do we evaluate cos(36) or simplify more?

Answer 18

Evaluate.

Answer 19

ok. is this straightforward or something we fancily work out?

Answer 20

very fancy :|

Answer 21

let x = 36
5x = 180
3x = 180 - 2x
sin 3x = sin2x
3 sinx - 4sin^3 x = 2sinx cox
Since sinx =/= 0
3- 4 sin^2 x = 2cosx
3- 4 ( 1-cos^2 x) = 2 cos x
4 cos^2 x - 2cosx -1 =0
Now, solve for cosx.

Answer 22

wow

Answer 23

@apple_pi Come back :'(

Answer 24

So in what class do we learn to play with this trick?

Answer 25

I'm sorry, I don't know. I'm not from the US. But for me, I learnt it two years before university.

Answer 26

Sorry... I had to go for a while

Answer 27

Yeah that solved it! Thanks @Callisto

Answer 28

You're welcome. FYI, this post is worth looking!
http://openstudy.com/study#/updates/4fe6e718e4b02c91101b52cd

Answer 29

Got another one:
http://openstudy.com/study#/updates/50827553e4b0dab2a5ebddaa