I have two problems where i am trying to prov there identities.
I think i am close but just not getting it. This isnt really homework. Its just practice problems that are not in the solutions manual.
1. prove the follwoing identities.
b) sec(x)(tan(x) + cot(x)) = csc(x) / cos^2(x)
This is what i have so far,
this is close to the identity. can i split it up so its 1/cos^2(x) times 1/ sin(x) ?
and now for part c - Note x = theta. i just didnt want to type it out..
c) Tan(x) - cot(x) / tan(x) + cot(x) = sin^2(x) - cos^2(x)
This is what i have so far,
I dont know what to do from here..
I think i am close but just not getting it. This isnt really homework. Its just practice problems that are not in the solutions manual.
1. prove the follwoing identities.
b) sec(x)(tan(x) + cot(x)) = csc(x) / cos^2(x)
This is what i have so far,
Code:
= 1/ cos(x) times sin(x) / cos(x) + 1/tan
= 1/ cos(x) times sin(x) / cos(x) + cos(x) / sin(x)
= 1/ cos(x) times sin^2(x) / cos(x) + cos^2(x) / sin(x) // just like adding fractions
Since sin^2x + cos^2x = 1
1/cos(x) times 1 / cos(x) sin(x)
1/cos^2(x) sin(x)
and now for part c - Note x = theta. i just didnt want to type it out..
c) Tan(x) - cot(x) / tan(x) + cot(x) = sin^2(x) - cos^2(x)
This is what i have so far,
Code:
= sin (x) / cos(x) - cos(x) / sin(x) big divided by cos(x) / cos(x) + cos(x) / sin(x)
= sin^2(x) - cos^2(x) / cos(x)sin(x) big divided by sin^2(x) + cos^2(x) / cos(x)sin(x)
Now, since cos^2(x) + sin^2(x) = 1
= 1 / cos(x) - sin(x) / 1 / cos(x) + sin(x)
= 1 / cos(x) - sin(x) times cos(x) + sin(x) / 1
ones cancel out. Now, since theres a negative and a positive between them i cant cancel?
So, i am left with cos(x) + sin(x) / cos(x) - sin(x)
if i can combine them somehow i have the right identity
What did i do so wrong?
I dont know what to do from here..