Question

f(sinx+1/sinx)=csc^2x-cos^2x 求f(x)

Answer 1

f(sinx+1/sinx)=csc^2x-cos^2x

=1/sin^2x-cos^2x

=1/sin^2x-(1-sin^2x)

=1/sin^2x+sin^2x-1

=1/sin^2x+2+sin^2x-1-2

=(sinx+1/sinx)^2-3

f(x)=x^2-3