Given that tan(pi/2) = a. Express tan(x) and sin(x) in terms of a. Hint: Use the fact that x = 2.(pi/2)

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tan(π/2) is undefined.

oh it's tan(x/2) = a ........... use the fact that x = 2 . x/2

To express tan(x) and sin(x) in terms of a, we can start by using the given information: tan(pi/2) = a.

Since x = 2.(pi/2), we can rewrite x as pi. Therefore, we need to express tan(pi) and sin(pi) in terms of a.

Now, let's look at the values of the trigonometric functions at pi:

1. tan(pi):
Recall that the tangent function is periodic with a period of pi. Therefore, tan(pi) is equal to tan(0), which is 0. So, tan(pi) = 0.

2. sin(pi):
The sine function is an odd function, meaning that sin(-x) = -sin(x) for any x. Since sin(0) = 0, we can conclude that sin(pi) = -sin(0) = 0.

Therefore, we have tan(pi) = 0 and sin(pi) = 0.

Substituting these values into the expressions, we can say that:

tan(x) = tan(pi) = 0,
sin(x) = sin(pi) = 0.

Hence, we can express tan(x) = 0 and sin(x) = 0 in terms of a.