SOLUTION: Simplify the following expressions as much as possible. cos(x+pi/3)+sin(x-pi/6)

Algebra.Com
Question 1138453: Simplify the following expressions as much as possible.
cos(x+pi/3)+sin(x-pi/6)

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Use the identity cos(A+B) = cos(A)*cos(B) - sin(A)*sin(B)









-------------------------------

Use the identity sin(A-B) = sin(A)*cos(B) - cos(A)*sin(B)













note how this result is basically the negative version of the result from the previous section above.

-------------------------------



Let y = cos(x)-sqrt(3)*sin(x)







-------------------------------

Answer: The original expression simplifies to 0

We can say that the equation is an identity, meaning that it is a true equation for all real numbers x.

RELATED QUESTIONS

Simplify the following expressions as much as possible.... (answered by jim_thompson5910)
Verify following is an identity. sin((x)+(pi/3))-cos((x)+(pi/6))=sin(x) (answered by Tatiana_Stebko)
prove... (answered by Fombitz)
Solve the following trigonometric equation analytically (using identities if necessary... (answered by stanbon)
If cos(x+pi/6)+sin(x−pi/3)=A, then the number... (answered by lwsshak3)
write the expression as sine, cosine or tangent of a single angle. cos(pi )/(6)cos(pi... (answered by ikleyn)
1) Find the exact value of (Sin 130*)(cos 132*)+(cos 138*)(sin 132*) 2) Simplify cos... (answered by Edwin McCravy)
(sin(x+pi))/(cos(x-pi)) (answered by stanbon)
For which of the following values of x is cos x/sin x not defined? A) Pi/2 B) Pi/3 C)... (answered by Fombitz,CharlesG2)