To simplify the function sectan(1x), it’s essential to first understand the terms involved:
- secant: In trigonometric functions, the secant function is defined as sec(x) = 1/cos(x).
- tangent: Similarly, the tangent function is defined as tan(x) = sin(x)/cos(x).
Therefore, sectan(1x) can be expressed as:
sectan(1x) = sec(1x) * tan(1x)Substituting the definitions of secant and tangent into this expression, we get:
sectan(1x) = (1/cos(1x)) * (sin(1x)/cos(1x))Combining these terms gives:
sectan(1x) = sin(1x) / (cos(1x) * cos(1x)) = sin(1x) / cos²(1x)In summary, the simplified form of sectan(1x) is:
sectan(1x) = sin(1x) / cos²(1x)This expression can be used for further computations or to derive more complex identities involving trigonometric functions.
Feel free to ask if you have any additional questions regarding trigonometric simplifications!