Answer:
cos (5π/14)
Step-by-step explanation:
The given expression is:
[tex]sin (\frac{\pi }{2})cos( \frac{\pi }{7})+cos (\frac{\pi }{2})sin( \frac{\pi }{7})[/tex]
The expression can be reduced by using the trigonometric identities
The suitable identity is:
cos (A - B) = cos A cos B + sin A sin B
Here A = π/2
B = π/7
Therefore,
[tex]sin (\frac{\pi }{2})cos( \frac{\pi }{7})+cos (\frac{\pi }{2})sin( \frac{\pi }{7}) = cos(\frac{\pi }{2} -\frac{\pi }{7} ) = cos(\frac{7\pi -2\pi }{14} ) = cos\ \frac{5\pi }{14}[/tex]
