Practicing Success
A line makes the same angle $\theta $, with each of the x and z-axes. If the angle $\beta $, which it makes with y-axis, is such that $sin^2 \beta = 3 sin^2 \theta , $ then $cos^2 \theta $ equals |
$\frac{2}{5}$ $\frac{1}{5}$ $\frac{3}{5}$ $\frac{2}{3}$ |
$\frac{3}{5}$ |
Let $l, m, n $ be the direction cos (lines. Then, $l = cos \theta , m = cos \beta $ and $ n = cos \theta $ $⇒ cos^2 \theta cos^2 \beta + cos^2 \theta = 1 $ $⇒ 2cos^2 \theta + 1 -sin^2 \beta = 1 ⇒ 2 cos^2 \theta - sin^2 \beta = 0 $ $⇒ 2 cos^2 \theta - 3 sin^2 \theta = 0 $ $[sin^2 \beta = 3 sin^2 \theta $(Given)] $⇒ tan^2 \theta = \frac{2}{3}$ $∴ cos^2\theta = \frac{1}{1+tan^2\theta }=\frac{1}{1+2/3}=\frac{3}{5}$ |