SOLUTION: If tan(x) + cot(x) = 144/25, what is the numerical value of 1/tan(x) + 1/cot(x)

Algebra ->  Trigonometry-basics -> SOLUTION: If tan(x) + cot(x) = 144/25, what is the numerical value of 1/tan(x) + 1/cot(x)      Log On


   

Question 1152724: If tan(x) + cot(x) = 144/25, what is the numerical value of 1/tan(x) + 1/cot(x)
Found 2 solutions by jim_thompson5910, ikleyn:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

The answer is 144/25

Why is this? Because
1%2Ftan%28x%29+=+cot%28x%29
and
1%2Fcot%28x%29+=+tan%28x%29

So +1%2Ftan%28x%29+%2B+1%2Fcot%28x%29 becomes cot%28x%29%2Btan%28x%29, in which we can rearrange the terms (because we can add two numbers in any order). So cot%28x%29%2Btan%28x%29 turns into tan%28x%29%2Bcot%28x%29 which was the original left hand side of the given equation.

Answer by ikleyn(52809) About Me  (Show Source):
You can put this solution on YOUR website!
.

To answer the question, recall that  1%2Ftan%28x%29 = cot(x)  and  1%2Fcot%28x%29 = tan(x).


Therefore,


    1%2Ftan%28x%29 + 1%2Fcot%28x%29 = cot(x) + tan(x) = ( commutativity of the addition operation ) = tan(x) + cot(x) = (as it is given) = 144%2F25.    ANSWER


Solved (!)

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Actually, it is a joke problem . . .