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
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
Answer this Question
- Mathematics - Trigonometric Identities - Let y represent theta Prove: 1 + 1/tan^...
- TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...
- tigonometry - expres the following as sums and differences of sines or cosines ...
- algebra - Can someone please help me do this problem? That would be great! ...
- Math - Calculus - The identity below is significant because it relates 3 ...
- trig - Reduce the following to the sine or cosine of one angle: (i) sin145*cos75...
- math - Proving Trigonometric Identities 1. sec^2x + csc^2x= (sec^2 x)(csc^2 x) 2...
- Trig - Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < ...
- pre-cal - Simplify the given expression........? (2sin2x)(cos6x) sin 2x and cos ...
- math - Can you please check my work. A particle is moving with the given data. ...