$\frac{1-tan25^{^{\circ}}}{1+tan25^{^{\circ}}}=$ কত ?

আমরা জানি, $tan(A-B) = \frac{tanA - tanB}{1 + tanA tanB}$ । এখানে, $tan45^{^{\circ}} = 1$ । সুতরাং, $\frac{1-tan25^{^{\circ}}}{1+tan25^{^{\circ}}} = \frac{tan45^{^{\circ}}-tan25^{^{\circ}}}{1+tan45^{^{\circ}}tan25^{^{\circ}}} = tan(45^{^{\circ}}-25^{^{\circ}}) = tan20^{^{\circ}}$ । আবার, $tan(90^{^{\circ}}-\theta) = cot\theta$ । তাই, $tan20^{^{\circ}} = tan(90^{^{\circ}}-70^{^{\circ}}) = cot70^{^{\circ}}$ । সুতরাং, $\frac{1-tan25^{^{\circ}}}{1+tan25^{^{\circ}}} = cot70^{^{\circ}}$ ।