Question

求证1/（sin^2)a+1/(cos^2)a-1/(tan^2)a=2+(tan^2)a

Answer 1

左边=1/[(sin^2)a(cos^)a]-(cos^2)a/(sin^2)a

=[1-(cos^4)a]/[(sin^2)a(cos^2)a]

=[1+(cos^2)a] [1-(cos^2)a]/[(sin^2)a(cos^2)a]

=[1+(cos^2)a]/(cos^2)a

= [(sin^2)a+(cos^2)a+(cos^2)a]/(cos^2)a

=[(sin^2)a+2(cos^2)a]/(cos^2)a

=(tan^2)a+2=右边