Question

The distance between the points (cos θ, sin θ) and (sin θ, –cos θ) is

(a) √3 

(b) √2 

(c) 1 

(d) 0

Answer 1

(b) \(\sqrt2\)

Reqd. dist. = \(\sqrt{(sin\,\theta-cos\,\theta)^2+(-cos\,\theta-sin\,\theta)^2}\)

= \(\sqrt{(sin\,\theta-cos\,\theta)^2+(-cos\,\theta-sin\,\theta)^2+(cos^2\,\theta+2cos\,\theta\,sin\,\theta+sin^2\,\theta)}\)

= \(\sqrt{2(sin^2\,\theta+cos^2\,\theta)}\) = \(\sqrt2\) (∵ cos² θ + sin² θ = 1)