Question

How do you prove `[cosx/(1-sinx)] + [(1-sinx)/cosx]=2secx`?

Answer 1

Just add like ordinary fractions. LCD is (1-sinx)cosx. The sum would be `(cos^2x +1-2sinx +sin^2x)/[(1-sinx)cosx]`

=`(2-2Sin x)/[(1-sinx)cosx]`

=`2/cosx`

=2secx