SOLUTION: I need to verify the following trigonometric identity, while only working only the left or right side of the equation and leaving either the right or left side unchanged. 1/1+co

Algebra ->  Trigonometry-basics -> SOLUTION: I need to verify the following trigonometric identity, while only working only the left or right side of the equation and leaving either the right or left side unchanged. 1/1+co      Log On


   

Question 325256: I need to verify the following trigonometric identity, while only working only the left or right side of the equation and leaving either the right or left side unchanged.
1/1+cos theta + 1/1-cos theta = 2 + 2 cot^2 theta
I can make each side equal 2csc^2 theta currently, but have no clue how to make them equal working only one side. Thanks for taking the time to look at this, its appreciated.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
... Start with the given equation.


... Multiply the first fraction by %281-cos%28theta%29%29%2F%281-cos%28theta%29%29


... Multiply the second fraction by %281%2Bcos%28theta%29%29%2F%281%2Bcos%28theta%29%29


... Add the fractions.


... Combine like terms.


... FOIL the denominator.


... Use the identity


... Rewrite 2 as 2*1


... Use the identity (replace the "1" with the left side)


... Distribute.


... Break up the fraction.


... Reduce and use the identity cot%28theta%29=cos%28theta%29%2Fsin%28theta%29