How do you find the exact functional value sin(60˚+45˚) using the cosine sum or difference identity?

1 Answer
Aug 14, 2015

# sin (60^@ + 45^@) = (sqrt(3) + 1)/(2sqrt(2)) #

Explanation:

Using the sine identity:
# sin (A +- B) = sin A cos B +- cos A sin B #

# sin (60^@ + 45^@) = sin 60^@ cos 45^@ + cos 60^@ sin 45^@ #
# = sqrt(3)/2 xx 1/sqrt(2) + 1/2 xx 1/sqrt(2) = (sqrt(3) + 1)/(2sqrt(2)) #

If you want to use the cosine identity:
# cos (A +- B) = cos A cos B ""_+^(-) sin A sin B #

# sin A = cos (A-90^@) #

# sin (60^@+45^@) = cos (60^@ - 45^@) #
# = cos 60^@ cos 45^@ + sin 60^@ sin 45^@ #
# = 1/2 xx 1/sqrt(2) + sqrt(3)/2 xx 1/sqrt(2) #
# = (sqrt(3) + 1)/(2sqrt(2)) #