Question

Prove that $\sqrt{\frac{1+\cos \theta }{1-\cos \theta }}=\csc \theta +\cot \theta ;0\le \theta \le {90}^o.$

Answer 1

$\sqrt{\frac{1+cosx}{1-cosx}}$

$=\sqrt{\frac{1+cosx}{1-cosx}\times \frac{1+cosx}{1+cosx}}$

$=\sqrt{\frac{(1+cosx{)}^2}{1-co{s}^{2}x}}$

$=\sqrt{(\frac{1+cosx}{sinx}{)}^2}$

$=\frac{1+cosx}{sinx}$

$=cosecx+cotx$