Answer:
Option (2)
Step-by-step explanation:
Given trigonometric expression is,
[tex]\text{cos}(\frac{11\pi}{21})\text{cos}(\frac{\pi}{7})-\text{sin}(\frac{11\pi}{21})\text{sin}(\frac{\pi}{7})[/tex]
This expression is in the form of an identity,
cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
By substituting the values of A = [tex]\frac{11\pi}{21}[/tex] and B = [tex]\frac{\pi}{7}[/tex] in the identity,
[tex]\text{cos}(\frac{11\pi}{21})\text{cos}(\frac{\pi}{7})-\text{sin}(\frac{11\pi}{21})\text{sin}(\frac{\pi}{7})[/tex] = cos[tex](\frac{11\pi}{21}+\frac{\pi}{7})[/tex]
= cos[tex](\frac{11\pi+3\pi}{21})[/tex]
= cos[tex](\frac{14\pi}{21})[/tex]
= cos[tex](\frac{2\pi}{3})[/tex]
= -[tex]\frac{1}{2}[/tex]
Therefore, Option (2) will be the answer.
