Question

(Cos 5° + sin 25°)/(cos 25° - sin 5°)
Urgent va rog! :(

Answer 1

$\dfrac{cos5^{o}+sin25^{o}}{cos25^{o}-sin5^{o}}=\dfrac{sin85^{o}+sin25^{o}}{sin65^{o}-sin5^{o}}=\dfrac{2sin\dfrac{85^{o}+25^{o}}{2}\cdot cos\dfrac{85^{o}-25^{o}}{2}}{2sin\dfrac{65^{o}-5^{o}}{2}\cdot cos\dfrac{65^{o}+5^{o}}{2}}=\\\\=\dfrac{sin55^{o}\cdot cos30^{o}}{sin30^{o}\cdot cos35^{o}}=\dfrac{sin55^{o}\cdot cos30^{o}}{sin30^{o}\cdot sin55^{o}}=\dfrac{\sqrt3}2\cdot\dfrac{2}1=\sqrt3$