Complementary function to sec(x)
To find the complementary function to sec(x), we need to first understand what a complementary function is
To find the complementary function to sec(x), we need to first understand what a complementary function is.
In mathematics, given a function f (x), the complementary function is generally denoted as g(x) and is defined as the reciprocal of f(x) or the inverse of f(x).
In this case, the function f(x) is sec(x), which represents the secant of x.
The secant function, sec(x), is defined as the reciprocal of the cosine function, so we can express it as:
sec(x) = 1/cos(x)
To find the complementary function, g(x), we need to take the reciprocal of sec(x):
g(x) = 1/sec(x)
Since sec(x) is equal to 1/cos(x), we can substitute it into the expression:
g(x) = 1/(1/cos(x))
To simplify the expression, we can multiply the numerator and denominator by cos(x):
g(x) = cos(x)/(1/cos(x))
By multiplying the numerator and denominator, we get:
g(x) = cos^2(x)
Thus, the complementary function to sec(x) is cos^2(x).
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