The signature splittings in $K^{\pi} =1^{+}: 7/2[404]_{\pi}\bigotimes 9/2[624]_{\nu}$ , $K^{\pi} =0^{−}: 9/2[514]_{\pi}\bigotimes 9/2[624]_{\nu}$ bands of $^{180}$Ta and $K^{\pi} = 0^{−}: 7/2[404]_{\pi}\bigotimes 7/2[503]_{\nu}$ , $K_{\pi} = 1^{−}: 5/2[402]_{\pi}\bigotimes 3/2[512]_{\nu$ , $K^{\pi} = 1^{+}: 7/2[404]_{\pi}\bigotimes9/2[624]_{\nu}$ bands of $^{182}$Ta are analysed within the framework of two-quasiparticle rotor model. The phase as well as magnitudeof the experimentally observed signature splitting in $K^{\pi} = 1^{+}$ band of $^{180}$Ta, which could not be explained in earlier calculations, is successfully reproduced. The conflict regarding placement of a 12$^+$ level in $K^{\pi} = 1^{+}: 7/2+[404]_{\pi}\bigotimes 9/2+[624]_{\nu}$ ground-state rotational band of $^{180}$Ta is resolved and tentative nature of $K^{\pi} = 0^{−}:7/2[404]_{\pi}\bigotimes7/2[503]_{\nu}$ ,$K^{\pi} = 1^{+}: 7/2[404]_{\pi}\bigotimes 9/2[624]_{\nu}$ bands observed in $^{182}$Ta is confirmed. As a future prediction for experimentalists, these two-quasiparticle structures observed in $^{180}$Ta and $^{182}$Ta are extended to higherspins.