Prove or disprove?
posted by Jerry .
cos(X+pi/6) + sin(xpi/3) = 0
I am working with one side but I am not sure if I can subtract at all here.

Prove or disprove? 
Reiny
To see if it is an identity, pick any value of x
e.g. x = 78°
then x+π/6 > 78+30 = 108°
and xπ/3 > 78  60 = 18°
is cos108 + sin18 = 0 ???
YES
ok, then , let's prove it
LS = cosxcosπ/6  sinxsinπ/6 + sinxcosπ/3  cosxsinπ/3
= √3/2 cosx 1/2 sinx + 1/2 sinx  √3/2 cosx
= 0
= RS 
Prove or disprove? 
Steve
or, since we know that cos(pi/2  x) = sin(x)
cos(pi/2  (x+pi/6)) = sin(pi/3  x) = sin(xpi/3)
Respond to this Question
Similar Questions

math
Prove that for all real values of a, b, t (theta): (a * cos t + b * sin t)^2 <= a^2 + b^2 I will be happy to critique your work. Start on the left, square it, (a * cos t + b * sin t)^2 = a^2 (1  sin^2t) + 2ab sin t cost+ b^2 (1 … 
trig
it says to verify the following identity, working only on one side: cotx+tanx=cscx*secx Work the left side. cot x + tan x = cos x/sin x + sin x/cos x = (cos^2 x +sin^2x)/(sin x cos x) = 1/(sin x cos x) = 1/sin x * 1/cos x You're almost … 
Mathematics  Trigonometric Identities
Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) = (sin^2y … 
TRIG!
Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1  (3/4)sin^2 2x work on one side only! Responses Trig please help!  Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 … 
Precalc
Prove or disprove the following identity. cos(x)  sin(x) = cos(x) + sin(x) 
Prove or Disprove
Cos(X+y)cos(xy)= cos^2theta  sin^2theta I foiled the left side as a start because I can kind of see sin^2+cos^2=1 but I can't finish. 
Precalculus with Trigonometry
Prove or disprove the following identity: (sin(10x))/(sin(x)+sin(9x)) = (cos(5x))/(cos4x)) 
Precalculus with Trigonometry
Prove or disprove the following Identities: cos(x)  sin(x) = cos(x) + sin (x) sin raised to the 4 (theta)  cos raised to the 4 (theta) = sin squared (theta)  cos squared (theta) cos (x+(pi)/(6)) + sin (x  (pi)/(3)) = 0 cos(x+y)cos(xy) … 
Trigonometry desperate help, clueless girl here
2. solve cos 2x3sin x cos 2x=0 for the principal values to two decimal places. 3. solve tan^2 + tan x1= 0 for the principal values to two decimal places. 4. Prove that tan^2(x) 1 + cos^2(x) = tan^2(x) sin^2 (x). 5.Prove that tan(x) … 
MATH
Hi, I really need help with these questions. I did some of them halfway, but then I got stuck. Would you please help me?