求值[2sin50°+sin10°(1+√3tan10°)]*√2(sin80°)*(sin80°)
问题描述:
求值[2sin50°+sin10°(1+√3tan10°)]*√2(sin80°)*(sin80°)
答
注:题目似乎多乘了一个sin80°!
[2sin50°+sin10°(1+√3tan10°)]*√2(sin80°)
=[2sin50°+sin10°(1+√3tan10°)]*√2(cos10°)
=√2*[2sin50°cos10°+sin10°(cos10°+√3sin10°)]
=√2*[2sin50°cos10°+2sin10°(1/2 *cos10°+√3/2 *sin10°)]
=√2*(2sin50°cos10°+2sin10°cos50°)
=2√2*sin60°
=√6
当然如果题目中是(sin80°)*(sin80°),最后结果为√6cos10° (或√6sin80°)