△函数计算题求简便过程求值：（1-tan7°-tan8°-tan7°tan8°)/（1+tan7°+tan8°-tan7
2个回答
（1-tan7°-tan8°-tan7°tan8°)/（1+tan7°+tan8°-tan7°tan8°)
=[(tan7+tan8)/tan(7+8)-(tan8+tan7)] / [(tan7+tan8)/tan(7+8)+(tan8+tan7)]
=(tan7+tan8)(1/tan15-1) / (tan7+tan8)(1/tan15+1)
=(1-tan15) / (1+tan15)
=(cos15-sin15) / (cos15+sin15)
=(cos15-sin15)^2 / [(cos15+sin15)(cos15-sin15)]
=[(cos15)^2+(sin15)^2-2cos15sin15]/[(cos15)^2-(sin15)^2]
=(1-sin30)/cos30
=(1-1/2) / (√3/2)
=1/√3
=√3/3
