Question

i don't know if this is a hard one...but it LOOKS complicated ;D

Prove that:

\[\mathbf{\frac {cos (7A) + cos (3A) - cos (5A) - cos(A)}{sin(7A) - sin(3A) - sin (5A) + sin(A)} = cot(2A)}\]

Answer 1

is it o.O

Answer 2

Identity

Answer 3

It's not a formula..you have to like prove it..there's no formula for cot(x+y) i guess.

Answer 4

nahh i'll just change it...if it's like a formula then it's easy

Answer 5

Its an IDENTITY!!

Answer 6

Maybe you derive it the same way you derive tan(x+y).

Answer 7

yeh we need to open by the formula {(cos(x+y)}/sin(x+y)}

Answer 8

Yeah ^

Answer 9

i think that's not a formula anymore

Answer 10

LOl you can't change the question like that

Answer 11

fine i'll post in a different question :P

Answer 12

No need

Answer 13

lol, that is a very long proof..will take ages to type..

Answer 14

Using cosx+cosy & cosx-cosy identity

Answer 15

then sinx-siny & sinx+siny

Answer 16

long proof..ha! i knew it was hard \m/

Answer 17

probably double angle formulae..

Answer 18

its not hard, its just we dont have such time to waste on the latex :P

Answer 19

like wasoo knows how to use latex. :P

Answer 20

hehe thats another case :P but i learned it :P

Answer 21

lol, then use it to solve this problem. :P

Answer 22

across taught me i guess :P

Answer 23

sinX + sinY = 2sin[ (X + Y) / 2 ] cos[ (X - Y) / 2 ]
sinX - sinY = 2cos[ (X + Y) / 2 ] sin[ (X - Y) / 2 ]
cosX + cosY = 2cos[ (X + Y) / 2 ] cos[ (X - Y) / 2 ]
cosX - cosY = - 2sin[ (X + Y) / 2 ] sin[ (X - Y) / 2 ]

Answer 24

\[\huge \mathbf{L} \mathsf{A} \mathbf{T} \mathsf{E} \mathbf{X?}\]

Answer 25

hehe =))

Answer 26

@Diyadiya are you taking trig now? for you to remember those...

Answer 27

i've been doing trig since last 3yrs :D

Answer 28

\[\cot2A = \frac{\cos2A}{\sin2A} =\frac{2\cos^{2}A-1}{2sinAcosA} \]
I'm doubting that it is provable..

Answer 29

IDK .. LGB Type down what you did till now :D

Answer 30

http://www.wolframalpha.com/input/?i=%28cos%287a%29%2Bcos%283a%29-cos%285a%29-cos%28a%29%29%2F%28sin%287a%29-sin%283a%29-sin%285a%29%2Bsin%28a%29%29

Answer 31

proving is hard isnt it @_@

Answer 32

i mean tiresome

Answer 33

Looks like it would work..but will take a while..

Answer 34

any ideas diya?

Answer 35

well, we know that: \(\cos3x = 4\cos^{2} x-3cosx\) but what about cos(7x)?