三角函数 急f(x)=8sinx-tanx求f(80)-4cos10的值

三角函数 急f(x)=8sinx-tanx求f(80)-4cos10的值
三角函数 急
f(x)=8sinx-tanx
求f(80)-4cos10的值

三角函数 急f(x)=8sinx-tanx求f(80)-4cos10的值
f(80)-4cos10
=8sin80-tan80-4cos10
=8cos10-cot10-4cos10
=4cos10-cos10/sin10
=(4sin10cos10-cos10)/sin10
=(2sin20-cos10)/sin10
=(sin20+cos70-cos10)/sin10.(1)
=(sin20-sin40)/sin10.(2)
=-2cos30sin10/sin10
=-√3
注：(1),(2)两步应用和差化积公式,

8sin80-tan80-4cos10
=8cos10-tan80-4cos10
=4cos10-cot10
=4cos10-cos10/sin10
=(4sin10cos10-cos10)/sin10
=(2sin20-cos10)/sin10
=(sin20+sin20-sin80)/sin10
=[sin20+2cos50sin(-30)]/sin10
=(sin20-cos50)/sin10
=(sin20-sin40)/sin10
=2cos30sin(-10)/sin10
=-√3

f(80)-4cos10
=8sin80-tan80-4cos10
=8cos10-cot10-4cos10
=4cos10-cos10/sin10
=(4sin10cos10-cos10)/sin10
=(2sin20-cos10)/sin10
=(sin20+cos70-cos10)/sin10.....(1)
=(sin20-sin40)/sin10...........(2)
=-cos10/sin10
=-cot10