tan(π/2-x)
To find the value of tan(π/2 – x), we can use the trigonometric identity: tan(A – B) = (tan A – tan B)/(1 + tan A * tan B)
To find the value of tan(π/2 – x), we can use the trigonometric identity: tan(A – B) = (tan A – tan B)/(1 + tan A * tan B).
In this case, let A = π/2 and B = x. So, we have:
tan(π/2 – x) = (tan π/2 – tan x)/(1 + tan π/2 * tan x)
Now, let’s evaluate each term separately.
1. tan π/2:
The tangent of π/2 is infinity, or undefined. This is because at π/2, the angle is in a vertical position, and the tan function is not defined for angles where the cosine equals zero.
2. tan x:
This represents the tangent of the angle x.
3. tan π/2 * tan x:
Since tan π/2 is undefined, multiplying it by any other value will also result in an undefined value.
Now, let’s substitute these values back into the equation:
tan(π/2 – x) = (undefined – tan x)/(1 + undefined * tan x)
Since we have an undefined value in the equation, the expression tan(π/2 – x) is also undefined.
In summary, the value of tan(π/2 – x) is undefined due to the undefined values of tan π/2 and tan π/2 * tan x.
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