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.

Step 1: Understand the condition for continuity. For a function f(x) to be continuous at x=0, the limit of the function as x approaches 0 must be equal to the function's value at x=0. Given f(0) = a, we must have: a = _x 0 f(x) Step 2: Simplify the function f(x). The given function is f(x) = ظا س + ظا سجا س for x ≠ 0. This can be written as: f(x) = (2 x)/( x) Step 3: Evaluate the limit. Substitute the simplified function into the limit expression: a = _x 0 (2 x)/( x) Recall that x = ( x)/( x). Substitute this identity into the expression: a = _x 0 (2 ( x)/( x)) x Since x ≠ 0, x ≠ 0, so we can cancel x from the numerator and denominator: a = _x 0 (2)/( x) Step 4: Substitute x=0 into the simplified limit expression. a = (2)/((0)) We know that (0) = 1. a = (2)/(1) a = 2 The value of a is 2. Comparing this with the given options, option 2 is 2. The final answer is 2.