If cos x = \(\sqrt{\frac{a}{b}}\) find cosec x
A
\(\frac{b}{\sqrt{b - a}}\)
B
\(\sqrt{\frac{b}{a}}\)
C
\(\sqrt{\frac{b}{b - a}}\)
D
\(\sqrt{\frac{b - a}{a}}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
cosx = \(\sqrt{\frac{a}{b}}\)
y2 + \(\sqrt{(a)^2}\) = \(\sqrt{(b)^2}\) by pythagoras
y2 = b - a
∴ y = b - a
cosec x = \(\frac{1}{sin x}\) = \(\frac{1}{y}\)
\(\frac{b}{y}\) = \(\frac{\sqrt{b}}{\sqrt{b - a}}\)
= \(\sqrt{\frac{b}{b - a}}\)
Source: Myschool Past Questions Archive (Record #31422)