三角函数化简(1)1/(sin10°)-√3/(cos10°);(2)sin40°(tan10°-√3).

Question

三角函数 化简
(1) 1/(sin 10°)-√3/(cos 10°);
(2) sin 40°(tan 10°-√3).

Answer 1

(1) 1/(sin 10°)-√3/(cos 10°)
=(cos 10°-√3sin 10°)/sin 10°*cos 10°
=2(1/2cos 10°-√3/2sin 10°)/sin 10°*cos 10°
=2sin (30°-10°)/sin 10°*cos 10°
=2sin 10°*cos 10°/sin 10°*cos 10°
=2