Question

144/sin^2(x) * [sin^2(x+30度) + sin^2(x-30度)]

Answer 1

144/sin^2(x)*[（sinxcos30+cosxsin30）^2+(sinxcos30-cosxsin30)^2]

=144/sin^2(x)*[(根号3/2*sinx+1/2*cosx)^2+(根号3/2*sinx-1/2*cosx)^2]

=144/sin^2(x)*[3/4*sin^2(x)+根号3/2*sinxcosx+1/4*cos^2(x)+3/4*sin^2(x)-根号3/2*sinxcosx+1/4*cos^2(x)]

=144/sin^2(x)*(3/2*sin^2(x)+1/2*cos^2(x))

=144/sin^2(x)*3/2*sin^2(x)+144/sin^2(x)*1/2*cos^2(x)

=72(3+cos^2(x)/sin^2(x)*)

=72[3+cot^2(x)]

那么辛苦希望多加分