Trigonometry write tan in terms of cosec
oh my csc = 1/sin as I remember
so
sin = 1/csc
tan = sin/cos
but cos = sqrt(1-sin^2)
so
tan = sin/sqrt(1-sin^2
= 1/csc / [ sqrt(1 - 1/cssc^2)]
multiply top and bottom by csc
tan = 1/ [sqrt( csc^2-1)]
To write tan in terms of cosec, we need to recall the definitions of these trigonometric functions.
The tangent function (tan) is defined as the ratio of the sine function (sin) to the cosine function (cos):
tan(x) = sin(x) / cos(x)
The cosecant function (cosec) is defined as the reciprocal of the sine function:
cosec(x) = 1 / sin(x)
To express tan in terms of cosec, we can substitute the definition of cosec into the definition of tan:
tan(x) = sin(x) / cos(x)
= 1 / (1 / sin(x))
= 1 / cosec(x)
Therefore, tan(x) can be written in terms of cosec(x) as:
tan(x) = 1 / cosec(x)