tan19°+tan41°+3tan19°tan41°的值为( ) A.3 B.1 C.33 D.-3
问题描述:
tan19°+tan41°+
tan19°tan41°的值为( )
3
A.
3
B. 1
C.
3
3
D. -
3
答
由两角和的正切公式可得tan(19°+41°)=tan19°+tan41°1−tan19°tan41°,∴tan19°+tan41°=tan(19°+41°)(1-tan19°tan41°)=tan60°(1-tan19°tan41°)=3(1-tan19°tan41°),∴tan19°+tan41°+3ta...