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How do you Prove sin x times sec x equals tan x?
Remember SecX = 1/CosX Substitute SinX X 1 /CosX = SinX / CosX = TanX
What is tangent x degrees equals 5?
tanx = 5x = tan-1(5) = arctan5x ~ 78.69
How do you write tanx in terms of tan0.5x?
Tanx can be written as tan0.5x by dividing it by 2. tanx1/2=tan0.5x --- I doubt that you can, since the tangent of the whole angle is a function of the tangent of the half-angle and of the secant of the whole angle. Please see the link.
Secx tanx - cosx cotx equals sinx?
I suggest you convert everything to sines and cosines, and then try to simplify. For example, sec x = 1 / cos x, tan x = sin x / cos x, etc. Then - depending on the problem requirements - you either verify whether they are always equal or not, or determine for what values of x they are equal.
How can arccot of tanx be simplified?
There is not much that can be done by way of simplification. Suppose arccot(y) = tan(x) then y = cot[tan(x)] = 1/tan(tan(x)) Now cot is NOT the inverse of tan, but its reciprocal. So the expression in the first of above equation cannot be simplified further. Similarly tan[tan(x)] is NOT tan(x)*tan(x) = tan2(x)
