Question

求值 sin²15°+cos²75°+sin15°cos75°=______．

Answer 1

原式=

1-cos30°

2

+

1+cos150°

2

+sin15°sin15°=1-

cos30°

2

+

cos150°

2

+sin215°=1-cos30°+

1

2

-

1

2

cos30°=1-

3

2

×

3

2

+

1

2

=

3

2

-

3 3

4

．
故答案为：

3

2

-

3 3

4

．