JAMB - Mathematics (1980 - No. 29)
Simplify the given expression \(\sqrt{\frac{1 - cos x}{1 + cos x}}\)
\(\frac{1 - cos x}{sin x}\)
1 - cos x
sin x
1 + cos x
\(\frac{1 + cos x}{sin x}\)
Vysvetlenie
\(\sqrt{\frac{1 - cos x}{1 + cos x}}\) = a
a2 = \(\frac{1 - cosx}{1 + cosx}\)
\(\frac{1 - cosx}{1 + cosx}\) = \(\frac{1 - cosx}{1 - cosx}\)
= \(\frac{(1 - cosx)^2}{cos^2 x}\)
a2 = \(\frac{(1 - cos x)^2}{sin^2 x}\)
a = \(\frac{1 - cos x}{sin x}\)
a2 = \(\frac{1 - cosx}{1 + cosx}\)
\(\frac{1 - cosx}{1 + cosx}\) = \(\frac{1 - cosx}{1 - cosx}\)
= \(\frac{(1 - cosx)^2}{cos^2 x}\)
a2 = \(\frac{(1 - cos x)^2}{sin^2 x}\)
a = \(\frac{1 - cos x}{sin x}\)