SOLUTION: Prove the identity {{{1 + 1/cosx=tan^2x/secx-1}}}

Algebra ->  Trigonometry-basics -> SOLUTION: Prove the identity {{{1 + 1/cosx=tan^2x/secx-1}}}       Log On


   

Question 1040747: Prove the identity
1+%2B+1%2Fcosx=tan%5E2x%2Fsecx-1
Found 2 solutions by Edwin McCravy, robertb:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

1+%2B+1%2Fcos%28x%29%22%22=%22%22tan%5E2%28x%29%2F%28sec%28x%29-1%29

Work with the right side

tan%5E2%28x%29%2F%28sec%28x%29-1%29

Use the identity 1%2Btan%5E2%28theta%29%22%22=%22%22sec%5E2%28theta%29
solved for tan%5E2%28theta%29%22%22=%22%22sec%5E2%28theta%29-1


%28sec%5E2%28x%29-1%29%2F%28sec%28x%29-1%29

Factor the numerator as the difference of two squares:

%28%28sec%28x%29-1%5E%22%22%29%28sec%28x%29%2B1%5E%22%22%29%29%2F%28sec%28x%29-1%29

Cancel the (sec(x)-1)'s:



sec%28x%29%2B1

Use the identity sec%28theta%29%22%22=%22%221%2Fcos%28theta%29

1%2Fcos%28x%29%2B1

Use the commutative property:

1%2B1%2Fcos%28x%29

Edwin

Answer by robertb(5830) About Me  (Show Source):