Question

State the restrictions on the variables for these trigonometric identities.
a)(1 + 2 sin x cos x)/ (sin x + cos x) = sin x + cos x
b) sin x /(1+ cos x) = csc x - cot x

Answer 1

generally, restrictions on variables are caused by denominators being zero
so in #1
sinx + cosx = 0 causes problems
sinx = -cosx
sinx/cosx = -1
tanx = -1 , x is in quadrants II or IV
x = 135 or 225 degrees
or 3pi/4 or 5pi/4 radians

#2.
first of all on the right side we have
cscx and cotx
sinxe cscx = 1/sinx, and cotx = cosx/sinx , whenever the sinx = 0 we have an undefined value
sinx = 0 for x = 0, 180 , and 360 degrees or 0, pi, 2pi radians

secondly we have to worry about 1+cosx
1 + cosx = 0
cosx = -1
x = 180 degrees or pi radians

so the restrictions are 0, pi, 2pi radians, or
0, 180 and 360 degrees