Question #23d29

Question

250 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-07T18:50:36

# -1/4 ( sqrt 6 +sqrt 2 )#

We must use the trigonometry identity;

#cos(A+B) = cosAcosB - sinAsinB#

Hence let #A= pi/4 # and #B =( 2pi) / 3#

Hence

#cos( pi/4 + (2pi)/3 ) = cos( pi/4 )cos ((2pi)/3 )- sin( pi/4 )sin ((2pi)/3) #

# = (sqrt2 /2 * -1/2) - (sqrt2 /2 * sqrt3 /2) #

# = - sqrt2 /4 - (sqrt6 / 4)#

Hence yielding;

# = -1/4 ( sqrt 6 +sqrt 2 )#