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
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

Related Questions

How do you state restrictions for a function? State any restrictions on the variables. 3y^2 - 3y/ y - 3 state the restrictions on the variables x/x-y would the restrictions be x be 1 and y be zero State the restrictions on the variables and then simplify each of the following expressions. A.) X... State the restrictions on the variables √𝑥 − 5 State the restrictions on the variables √6 − 5x given no other restrictions, what are the domain and range of the following function? f(x)=x^2-2x+2... state the restrictions for the expression: (3x+6)/[(x-5)(x-2)(x+2)] - (5x^2 - 25x)/[(x-5)(x-2)(x+2)... State any restrictions on the variable in the complex fraction. （（x-3）/(x+4)）/((x*2-1)/x) State the restrictions on the variable and classify the restrictions as removable or nonremovable. ...