Question

A line makes some angle q with each of the

x-axis and z-axis. If angle b, which it makes with y-axis, is such that sin²b = 3 sin²q, then cos²q equals –

• A. $\frac{2}{3}$
• B. $\frac{1}{5}$
• C. $\frac{3}{5}$
• D. $\frac{2}{5}$

Answer 1

Answer: (C)

$\frac{3}{5}$

Answer 2

cos² a + cos² b + cos² g = 1 …(1)

sin² b = 3 sin² q …(2)

In equation (1), a = b = q

\ cos² q + cos² q + cos² b = 1

\ cos² b = 1 – 2 cos²q

1 – sin² b = 1 – 2 cos² q

\ 2 cos² q = 3 sin² q

2 cos² q = 3 – 3 cos² q

Ž 5 cos² q = 3

cos² q = 3/5