Question

Find the value of : $tan{63}^{\circ }\times tan{27}^{\circ }$

Answer 1

$tan{63}^{\circ }tan{27}^{\circ }=tan({90}^{\circ }-{27}^{\circ })tan{27}^{\circ }$

$=cot{27}^{\circ }tan{27}^{\circ }$ $[\because tan(\pi /2-\theta )=cot\theta$ and $cot\theta =\frac{1}{tan\theta }]$

$=\frac{1}{tan{27}^{\circ }}\times tan{27}^{\circ }$

$=1$