Question

sin7°+cos15°sin8°cos7°?sin15°sin8°的值为2?32?3

sin7°+cos15°sin8°cos7°?sin15°sin8°的值为2?32?3．

Answer 1

sin7°+cos15°sin8°

cos7°?sin15°sin8°

＝

sin7°+cos(7°+8°)sin8°

cos7°?sin(7°+8°)sin8°

=

sin7°+(cos7°cos8°?sin7°sin8°)sin8°

cos7°?(sin7°cos8°+sin8°cos7°)sin8°

=

sin7°+cos7°cos8°sin8°?sin7°sin28°

cos7°?sin7°sin8°cos8°?sin28°cos7°

=

sin7°?sin7°sin28°+cos7°cos8°sin8°

cos7°?sin28°cos7°?sin7°sin8°cos8°

=

sin7°(1?sin28°)+cos7°cos8°sin8°

cos7°(1?sin28°)?sin7°sin8°cos8°

=

sin7°cos8°+cos7°sin8°

cos7°cos8°?sin7°sin8°

=

sin(7°+8°)

cos(7°+8°)

=tan15°=tan（45°-30°）=

tan45°?tan30°

1+tan45°tan30°

=

1? 3 3

1+ 3 3

=2?

3

，
故答案为：2?

3