Question

f(x)=(1+1/tanx)sin(x)^2+msin(x+45)sin(x-45)

当tan(a)=2时，f(a)=3/5,求m的取值

Answer 1

当 tana=2 时，sina/cosa=2，(sina)^2/(cosa)^2=4， 因此由 (sina)^2+(cosa)^2=1 即知 (sina)^2=4/5.
由积化和差公式： sin(x+45)sin(x-45) = -1/2cos2x.
由上述，tana=2，(sina)^2=4/5，所以由倍角公式可知 cos2a=1-2(sina)^2 = -3/5，从而 sin(a+45)sin(a-45) = -1/2cos2a = 3/10.
所以
3/5
=f(a)
=(1+1/tana)(sina)^2+msin(a+45)sin(a-45)
=(1+1/2)(4/5)+m(3/10)
由此可以解出 m = -2.

Answer 2

f(x)=(1+1/tanx)sin(x)^2+msin(x+45)sin(x-45)
=（1+1/tanx)sin(x)^2+msin(x+45)[-cos(x+45)]
=(1+1/tanx)sin(x)^2-msin(x+45)cos(x+45)
=(1+1/tanx)sin(x)^2-m/2*sin(2x+90)
=(1+1/tanx)sin(x)^2-m/2*cos2x
=3/2sin²x+msin²x-m/2
=（3/2+m）sin²x-m/2

tana=2 sin²a=4/5
f（a）=3/5
解得m=-2

Answer 3

这么简单的题目 要是不会 就去问 坤哥啊