sec^2 dx
The expression “sec^2 x” represents the square of the secant function of x
The expression “sec^2 x” represents the square of the secant function of x.
The secant function, denoted as “sec(x)”, is a trigonometric function that is defined as the reciprocal of the cosine function. Mathematically, it can be written as:
sec(x) = 1/cos(x)
The square of the secant function, “sec^2 x”, is obtained by squaring the value of sec(x). Therefore,
sec^2 x = (1/cos(x))^2 = 1/(cos^2(x))
This expression can also be written as:
sec^2 x = 1 + tan^2 x
This identity is derived from the Pythagorean identity for sine and cosine:
sin^2 x + cos^2 x = 1
By dividing both sides of the equation by cos^2 x, we get:
(sin^2 x / cos^2 x) + (cos^2 x / cos^2 x) = 1 / cos^2 x
This simplifies to:
tan^2 x + 1 = sec^2 x
So, in summary, sec^2 x represents the square of the secant function, which can be written as 1/(cos^2 x) or 1 + tan^2 x.
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