Answer
See explanation
Work Step by Step
By factoring out terms, the relation $\eta_{\mathrm{cc}}=\eta_{\mathrm{g}}+\eta_{\mathrm{s}}-\eta_{\mathrm{g}} \eta_{\mathrm{s}}$ can be expressed as
$$
\eta_{\mathrm{cc}}=\eta_{\mathrm{g}}+\eta_{\mathrm{s}}-\eta_{\mathrm{g}} \eta_{\mathrm{s}}=\eta_{\mathrm{g}}+\underbrace{\eta_{\mathrm{s}}\left(1-\eta_{\mathrm{g}}\right)}_{\substack{\text { Positive since } \\ \eta_{\mathrm{g}}<1}}>\eta_{\mathrm{g}}
$$ or $$
\eta_{\mathrm{cc}}=\eta_{\mathrm{g}}+\eta_{\mathrm{s}}-\eta_{\mathrm{g}} \eta_{\mathrm{s}}=\eta_{\mathrm{s}}+\underbrace{\eta_{\mathrm{g}}\left(1-\eta_{\mathrm{s}}\right)}_{\substack{\text { Positive since } \\ \eta_{\mathrm{s}}<1}}>\eta_{\mathrm{s}}
$$ Thus we conclude that the combined cycle is more efficient than either of the gas turbine or steam turbine cycles alone.
