its the inverse of cosecant theta.
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The derivative of (sin (theta))^.5 is (cos(theta))/(2sin(theta))
For such simplifications, it is usually convenient to convert any trigonometric function that is not sine or cosine, into sine or cosine. In this case, you have: sin theta / sec theta = sin theta / (1/cos theta) = sin theta cos theta.
sin (theta) = [13* sin (32o)]/8 = 13*0.529919264/8 = 0.861118804 [theta] = sin-1 (0.861118804) [theta] = 59.44o
The identity for tan(theta) is sin(theta)/cos(theta).
It is not! So the question is irrelevant.