tan(π/2-x)
To simplify the expression tan(π/2 – x), we can use the trigonometric identity:
tan(π/2 – x) = cot(x)
Where cot(x) represents the cotangent function of x
To simplify the expression tan(π/2 – x), we can use the trigonometric identity:
tan(π/2 – x) = cot(x)
Where cot(x) represents the cotangent function of x.
The cotangent function can be defined as the reciprocal of the tangent function:
cot(x) = 1 / tan(x)
Therefore, tan(π/2 – x) simplifies to cot(x) or 1/tan(x).
To illustrate this with an example, let’s say x = π/6:
tan(π/2 – π/6) = tan(π/3)
Now, using the definition of tan(x):
tan(π/3) = √3
Therefore, tan(π/2 – π/6) simplifies to cot(π/6) or 1/√3.
In conclusion, tan(π/2 – x) simplifies to cot(x) or 1/tan(x), which represents the cotangent function of x.
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