How do you simplify # sin 15° cos 75° + cos 15° sin 75°#?

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Answer 1 · 2018-03-01T23:35:35

1

#sin 15° cos 75° + cos 15 ° sin 75 °#
#=sin(15°+75°)=sin(90)=1#

Answer 2 · 2018-03-01T23:45:43

# "We have the answer:" #

# \qquad \qquad \qquad \qquad \quad sin15^@ cos75^@ + cos 15^@ sin75^@ \ = \ 1. #

# "The expression given matches the pattern of the formula for" #
# sin( x + y ). \ \ "Recall that formula:" #

# \qquad \qquad \qquad \qquad \quad \quad sin( x + y ) \ = \ sinx cosy + cos x siny. #

# "Now write it in the reverse direction:" #

# \qquad \qquad \qquad \qquad \quad \quad sinx cosy + cos x siny \ = \ sin( x + y ). #

# "Now, if in the reverse direction of that formula, we let:" #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad x = 15^@ \qquad "and" \qquad y = 75^@; #

# "we get:" #

# \qquad \qquad \quad sin15^@ cos75^@ + cos 15^@ sin75^@ \ = \ sin( 15^@ + 75^@ ). #

# "Thus:" #

# \qquad \qquad \quad sin15^@ cos75^@ + cos 15^@ sin75^@ \ = \ sin( 90^@ ) \ = \ 1. #

# "So we have the following simplification result:" #

# \qquad \qquad \qquad \qquad \quad sin15^@ cos75^@ + cos 15^@ sin75^@ \ = \ 1. #