Question

If a = cosα + sinα and b = cosα - sinα then √a/√b + √b/√a.

Answer 1

\(\frac{\sqrt a}{\sqrt b} + \frac {\sqrt b}{\sqrt a} = \frac{a + b}{\sqrt a \sqrt b}\)

\(= \frac{(\cos \alpha + \sin\alpha)+ (\cos \alpha - \sin\alpha)}{\sqrt{\cos^2 \alpha - \sin^2 \alpha}}\)

\(= \frac{2 \cos \alpha}{\sqrt{\cos2\alpha}}\)