sec2 x
d/dx tan x
The function secant is denoted by sec and is defined as the reciprocal of the cosine function, i.e., sec(x) = 1/cos(x). Therefore, if we are given sec(2x), we can find its value as follows:
sec(2x) = 1/cos(2x)
To simplify this expression, we need to use the double angle formula for cosine, which states:
cos(2x) = 2cos^2(x) – 1
Substituting this formula into the expression for sec(2x), we get:
sec(2x) = 1/[2cos^2(x) – 1]
This is the simplified form of sec(2x). However, sometimes we may need to simplify it further by using other trigonometric identities, depending on the context of the problem we are working on.
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