Few questions on proving identities

[VanKwisH]

Homework Statement

seca + csca
--------------- = seca*csca
sina + cosa

Homework Equations

no relevant equations

The Attempt at a Solution

How would i prove this ?? i know i break down the left side...
which is

1/cosa + 1/sina
---------------------
sina + cosa

 

[rocomath]

Now break down the right side to sines and cosines. From there, cross multiply the denominator of your right side to the left, from there it will simplify to 1.

 

[VanKwisH]

on the right side it's 1/cosa * 1/sina = 1 /cosasina right??

 

[rocomath]

Yes, that's correct. Now cross multiply.

 

[VanKwisH]

hmmm i did cross multiply and then i got .....
((cosa*sina /cosa ) + ( cosa*sina /sina)) / sina+cosa for the left side
and then for the right side i got sina+cosa / cosa*sina for the right side ... is that right??

 

[rocomath]

Yes, that's correct. Now simplify and L=R.

 

[VanKwisH]

alright for the left side i was able to get one but for the right side it doesn't seem right ...

sina + cosa / cosa*sina ... that doesn't equal 1 does it.?

 

[rocomath]

Sorry, all the writing confused me. The right side should only be sina+cosa, right? B/c you cross multiplied and so sinacosa disappears from the right.

 

[VanKwisH]

OOOOOOOOOOOO alright ... but that doesn't equal 1 though ... only sin^2a + cos^2 a = 1

 

[VanKwisH]

O wait but since i cross multiplied the denominator on the left side is gone as well right??

 

[HallsofIvy]

hmmm i did cross multiply and then i got .....
((cosa*sina /cosa ) + ( cosa*sina /sina)) / sina+cosa for the left side
and then for the right side i got sina+cosa / cosa*sina for the right side ... is that right??

I'm not sure what you mean by "cross multiply". To me, it means multiply both sides by the common denominator: here, that is (sin a cos a)(sin a+ cos a). You seem to have multiplied one side by (sin a+ cos a) and the other by (sin a cos a). Of course, that will not give you the same thing- you are multiplying the two sides by different things.

 

[VanKwisH]

I'm not sure what you mean by "cross multiply". To me, it means multiply both sides by the common denominator: here, that is (sin a cos a)(sin a+ cos a). You seem to have multiplied one side by (sin a+ cos a) and the other by (sin a cos a). Of course, that will not give you the same thing- you are multiplying the two sides by different things.

yahhh ... i messed up but i fixed it now and i got it ...
but i think cross multiplying is different for example

sinx cosx
------ ---------
cosx sinx

from what i know ... u would multiply the sinx on top by the one on the bottom ...
and the cosx by the cosx ... therefore u would have sin^2x and cos^2x ...
that's how i interpret it...unlesss i am completely wrong ...