# "Nice question !!" #
# "The pattern of the question matches the pattern of the rule for" #
# "the cosine of a sum/difference -- "#
# \qquad \qquad \qquad \qquad \quad cos( x - y ) \ = \ cosx cosy + sin x sin y. #
# "So:" #
# \qquad \qquad \qquad \qquad \quad cosx cosy + sin x sin y \ = \ cos( x - y ). #
# "So, with" \ x = 70, \quad y = 40, "we have:" #
# \qquad \qquad \qquad \qquad \quad cos70 cos40 + sin 70 sin 40 \ = \ cos( 70 - 40 ). #
# "Thus:" #
# \qquad \qquad \qquad \qquad \quad cos70 cos40 + sin 70 sin 40 \ = \ cos( 30 ). \qquad \qquad \qquad \qquad (I)#
# "But, recalling the 30-60-90 right triangle, we have:" #
# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad cos( 30 ) \ = \ \sqrt{3}/2. #
# "So, by (I):" #
# \qquad \qquad \qquad \qquad \quad cos70 cos40 + sin 70 sin 40 \ = \ \sqrt{3}/2. #
# "This is our answer -- nice question !!" #
