Question

answer with written proof

Answer 1

$\frac{Cos\: 70}{Sin\: 20} + \frac{Cos\: 59}{Sin\: 31}- 8Sin^{2}\: 30$

$Cos\: \theta = Sin\: (90-\theta)$

&
$Sin\: 30 = \frac{1}{2}$

=> $\frac{Sin\: (90-20)}{Sin\: 20} + \frac{Sin\: (90-31)}{Sin\: 31}- 8(\frac{1}{2})^{2}$

=> $\frac{Sin\: 20}{Sin\: 20} + \frac{Sin\: 31}{Sin\: 31}- 8(\frac{1}{4})$

= 1 + 1 - 2

= 0

Answer 2

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