Question

如果sin(α+20°)=cos(α+10°)+cos(α-10°),那么tanα的值是多少？求过程，麻烦大家了。

Answer 1

sin(α+20°)=cos(α+10°)+cos(α-10°),
展开得：sinαcos20°+cosαsin20°
= cosαcos10°-sinαsin10°+ cosαcos10°+sinαsin10°
sinαcos20°+cosαsin20°=2 cosαcos10°
sinαcos20°=cosα(2 cos10°- sin20°)
sinα/cosα=(2 cos10°- sin20°) / cos20°
tanα=(2 cos10°- sin20°) / cos20°
tanα=(2 cos10°- sin(30°-10°) ) / cos20°
tanα=(2 cos10°- (sin30°cos10°- cos30°sin10°) ) / cos20°
tanα=(2 cos10°- (1/2 cos10°-√3/2 sin10°) ) / cos20°
tanα=(3/2 cos10°+√3/2 sin10°) / cos20°
tanα=√3(√3/2 cos10°+1 /2 sin10°) / cos20°
tanα=√3sin(60°+10°)/ cos20°
tanα=√3.