Question
Evaluate: $\frac{\cot 54^{\circ}}{\tan 36^{\circ}}+\frac{\tan 20^{\circ}}{\cot 70^{\circ}}-2$
✓
Answer
$\frac{\cot 54^{\circ}}{\tan 36^{\circ}}+\frac{\tan 20^{\circ}}{\cot 70^{\circ}}-2 $
$ =\frac{\cot \left(90^{\circ}-36^{\circ}\right)}{\tan 36^{\circ}}+\frac{\tan \left(90^{\circ}-70^{\circ}\right)}{\cot 70^{\circ}}-2 $
$ =\frac{\tan 36^{\circ}}{\tan 36^{\circ}}+\frac{\cot 70^{\circ}}{\cot 70^{\circ}}-2$
$= 1 + 1 - 2$
$= 2 - 2$
$= 0$
$ =\frac{\cot \left(90^{\circ}-36^{\circ}\right)}{\tan 36^{\circ}}+\frac{\tan \left(90^{\circ}-70^{\circ}\right)}{\cot 70^{\circ}}-2 $
$ =\frac{\tan 36^{\circ}}{\tan 36^{\circ}}+\frac{\cot 70^{\circ}}{\cot 70^{\circ}}-2$
$= 1 + 1 - 2$
$= 2 - 2$
$= 0$
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