Question

求sec50°+tan10°的值．

Answer 1

分析：把原式先轉化成弦，再利用和差化積公式進行化簡，最后可得出答案．

解答：解：sec50°+tan10°
=

1

cos50°

+

sin10°

cos10°

=

2sin50°

2sin50°cos50°

+

sin10°

cos10°

=

2sin50°

sin100°

+

sin10°

cos10°

=

2sin50°

cos10°

+

sin10°

cos10°

=

2sin50°+sin10°

cos10°

=

sin50°+(sin50°+sin10°)

cos10°

=

sin50°+cos20°

cos10°

=

cos40°+cos20°

cos10°

=

2cos30°cos10°

cos10°

=2cos30°
=

3

點評：本題主要考查弦切互化的問題．要熟練掌握三角函數中的如和差化積、積化和差、倍角公式等常用公式．