Question

$frac{sin20 ^{0} + cos290 ^{0} }{2sin10^{0} * cos10 ^{0}}$

Answer 1

$frac{sin 20к+cos290к}{2sin10кcos10к} = frac{sin 20к+cos(270к+20к)}{2sin10кcos10к} =frac{sin 20к+sin20к}{sin 20к} = frac{2sin 20к}{sin20к}=2$

$sin2 alpha =2sin alpha cos alpha$
$cos(270к+ alpha)=sin alpha$