How do you find the exact value of cos ((2pi)/9) cos (pi/18)+sin ((2pi)/9) sin (pi/18)?

2 Answers

sqrt3/2

Explanation:

This is of the form cos(a-b)=cos (a)cos (b)+sin (a)sin (b)

The above expression simplifies to

cos (2pi/9 - pi/18)
cos (3pi/18)

cos (pi /6) = cos 30 = sqrt3/2

Dec 25, 2017

color (red)(sqrt3/2)

Explanation:

we know that
color (cyan)(cos (A-B)=cosA×cosB+sinA×sinB)
similarly the equation given is question can be written as
cos (2pi/9-pi/18)
cos ((4pi-pi)/18)
cos (3pi/18)
cos (pi/6)
cos ((180°)/6)
color (green)(cos (30°) = sqrt3/2)