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The function f(x) is defined as f(x) = (tan x + tan x) / sin x for x ≠ 0, and f(0) = a. Find the value of 'a' that makes the function continuous at x=0.
Mathematics
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Step-by-step solution
4 stepsUnderstand the condition for continuity.
For a function to be continuous at , the limit of the function as approaches 0 must be equal to the function's value at .
Given , we must have:Simplify the function .
The given function is for .
This can be written as:Evaluate the limit.
Substitute the simplified function into the limit expression:
Recall that . Substitute this identity into the expression:
Since , , so we can cancel from the numerator and denominator:
Substitute into the simplified limit expression.
We know that .
The value of is 2.
Comparing this with the given options, option 2 is 2.The final answer is .
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