SOLUTION: How do you solve these using Trigonometric Identities? (This is a fraction by the way): tan(x) + cot(x) ----------- ---- sec^2(x)

Algebra ->  Trigonometry-basics -> SOLUTION: How do you solve these using Trigonometric Identities? (This is a fraction by the way): tan(x) + cot(x) ----------- ---- sec^2(x)      Log On


   

Question 1155878: How do you solve these using Trigonometric Identities? (This is a fraction by the way):

tan(x) + cot(x)
----------------
sec^2(x)
Found 2 solutions by Edwin McCravy, MathLover1:
Answer by Edwin McCravy(20062) About Me  (Show Source):
You can put this solution on YOUR website!
It makes no sense to say "solve" a fraction.  The word is "simplify".
There is a lady on here who will "get you told" if you use improper
words.  So let's simplify, not "solve", the trigonometric expression.

%28tan%5E%22%22%28x%29+%2B+cot%5E%22%22%28x%29%29%2Fsec%5E2%28x%29 





Get LCD on the left, invert and change to multiplication on the right:



Use Pythagorean identity on top



Cancel the cos(x) into the cos²(x) and get cos(x) on top



cos%5E%22%22%28x%29%2Fsin%5E%22%22%28x%29

cot%5E%22%22%28x%29

Edwin

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
%28tan%28x%29+%2B+cot%28x%29%29%2Fsec%5E2%28x%29
use identities:
tan%28x%29=sin%28x%29%2Fcos%28x%29
cot%28x%29=cos%28x%29%2Fsin%28x%29
sec%5E2%28x%29=1%2Fcos%5E2%28x%29

then, you have

%28sin%28x%29%2Fcos%28x%29%2B+cos%28x%29%2Fsin%28x%29%29%2F%281%2Fcos%5E2%28x%29%29





%281%2F%28sin%28x%29cos%28x%29%29%29%2F%281%2Fcos%5E2%28x%29%29

cos%5E2%28x%29%2F%28sin%28x%29cos%28x%29%29

cos%5Ecross%282%29%28x%29%2F%28sin%28x%29cross%28cos%28x%29%29%29

cos%28x%29%2Fsin%28x%29

cot%28x%29