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

2 Answers
Sidharth · Chirag Mehta
Feb 16, 2016

#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#

Chirag Mehta
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)#

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