If\(\frac{cos2A+sin2A}{cosA-sinA}\)=1-sinA.k

find the value of k?

-2(1+\(\sqrt {3}\))

Put A = 30°

⇒ \(\frac{cos60°+sin60°}{cos30°-sin30°}\)=1- k sin30°

⇒ \(\frac{\frac{1}{2}+\frac{\sqrt {3}}{2}}{\frac{\sqrt {3}}{2}+\frac{1}{2}}\)=1-\(\frac{k}{2}\)

⇒ \(\frac{\sqrt {3}+1}{\sqrt {3}-1}\)=1-\(\frac{k}{2}\)

⇒ \(\frac{k}{2}\)=1-2-\(\sqrt {3}\)

⇒ k=-2(1+\(\sqrt {3}\))