Find an exact solution to the equation below so that 0 < x< pi
(1+tan(x)) / sin(x) = 0
ah, you mean trigonometric equation?
(1+tan(x)) / sin(x) = 0.
cross multiplying, 1 + tan x = 0
tan x = -1
x = arctan (-1)
x = -45 degrees = pi/4 radians
or if u want a family of solutions, x = (pi/4)(4k - 1), where k is an element of Z.
look at the graph
But what if (1 + tan x)/sin x = 0 is written this way,
surely sin x is included,
(1 + tan x)/sin x = (1 + tan x)(csc x) = 0, simplifying
csc x + sec x = 0,
csc x = - sec x
1/sin x = - 1/ cos x
sin x/cos x = tan x = -1, same as above.
but i really wonder why the graph of csc x + sec x behave differently,
see below,