Question

Help with trigonometry, establishing identities

Answer 1

rewrite everything in terms of sines and cosines, and add all fractions that are inside the fractions. This shouldn't be hard....

Answer 2

I'm trying, but still I'm not finding out the way to do it

Answer 3

what will you get for the numerator of the fraction on the left hand side?
what will you get for the numerator of the fraction on the right hand side?
what will you get for the denominator of the fraction on the left hand side?
what will you get for the denominator of the fraction on the right hand side?

answer each of these questions.

Answer 4

I just don't know how to continue after I get ((1+cos)/sin)/((1+sin)/cos)

Answer 5

this is the left side, do the right side

Answer 6

I have to make the left side equal to the right side, without changing the right side

Answer 7

ohh, I see.

Answer 8

I don't how t do it without changing the right side -:(

Answer 9

perhaps it would be good to first do it by manipulating both sides to see how to do it with using only one side.

Answer 10

I'm getting ((1+cos)/sin)/((1+sin)/cos) = ((1-sin)/cos)/(1-cos)/sin)
still I'm not having any idea

Answer 11

then after dividing the fractions on both sides you get (roughly )

( cos+cos² ) / (sin + sin² ) = (sin - sin²) / (cos - cos² )

then cross multiply that and I get,

(cos²-cos\(\normalsize\color{black}{ \rm ^4 }\)) / (sin²-sin\(\normalsize\color{black}{ \rm ^4 }\) )

factor the top out of cos², and the bottom out of sin². Then apply sin²+cos²=1
(as either cos²=... or sin²=.... )

and you get
cos²(sin²) = sin²(cos²)

Answer 12

I am not sure how to do it without touching the other side though... I always hated when I can only use one side .

Answer 13

Thanks very much, it seems that I would never find out the answer

Answer 14

it is very tricky, it is an identity though, but you have to show how it is an identity, without touching the other side. And that I can't do, sorry -:(

Answer 15

it's okay, I just needed to know if I was doing something wrong or it was really hard, because I'm studying for a final, and just got stuck on this one