im taking test
need answer quick'
use the sum and difference identities to write the expression as the cosine of the angle. be sure to simplify the anglee:
cospi/9cospi/3-sin
pi/9sinpi/3
You're taking a test? Do you want us to help you cheat??
My, goodness, no!!
hint:
cos(A+B) = cosAcosB - sinAsinB
To write the given expression using the sum and difference identities for cosine, we will use the following identities:
1. cos(A - B) = cos(A)cos(B) + sin(A)sin(B)
2. sin(A - B) = sin(A)cos(B) - cos(A)sin(B)
Let's break down the given expression step by step:
Expression: cos(pi/9)cos(pi/3) - sin(pi/9)sin(pi/3)
1. First, let's simplify the angles inside the trigonometric functions:
cos(pi/3) = 1/2
sin(pi/3) = sqrt(3)/2
2. Apply the sum and difference identities:
cos(pi/9)cos(pi/3) - sin(pi/9)sin(pi/3)
= (cos(pi/9) * (1/2)) - (sin(pi/9) * (sqrt(3)/2))
3. Simplify further:
= (1/2)cos(pi/9) - (sqrt(3)/2)sin(pi/9)
Therefore, the expression is simplified to:
cos(pi/9)cos(pi/3) - sin(pi/9)sin(pi/3) = (1/2)cos(pi/9) - (sqrt(3)/2)sin(pi/9)
Please note that the expression cannot be further simplified without knowing the specific values of cosine and sine for the angle pi/9.