Posted by **Emily** on Wednesday, December 22, 2010 at 6:02pm.

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

- Math -
**Reiny**, Wednesday, December 22, 2010 at 7:12pm
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

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