Question

计算：cos²75°+cos²15°+cos75°cos15°．

Answer 1

cos75°=cos（45°+30°）=cos45°cos30°-sin45°sin30°=

6 - 2

4

．
cos15°=cos（45°-30°）=cos45°cos30°+sin45°sin30°=

6 + 2

4

．
cos²75°+cos²15°+cos75°cos15°=cos²75°+sin²75°+

6 - 2

4

•

6 + 2

4

=1+

1

4

=

5

4

．