Question

三角函数求证 已知3/(sin20°）^2-1/(cos20°)^2=32cos40°

Answer 1

3/(sin20)^2-1/(cos20)^2

=[3(cos20)^2-(sin20)^2]/(sin20)^2(cos20)^2

=[(√3cos20+sin20)(√3cos20-sin20)]/(sin20cos20)^2

=[2sin(60+20)*2sin(60-20)]/[(sin40)/2]^2

=16sin80sin40/sin40*sin40

=16sin80/sin40

=32sin40cos40/sin40

=32cos40