If `sintheta=a/b`, then `costheta` is equal to

Options

A. `b/(sqrt(b^(2)-a^(a))`
B. `b/a`
C. `(sqrt(b^(2)-a^(2)))/b`
D. `a/(sqrt(b^(2)-a^(2))`

Answer

C

Explanation

Given, `sintheta=a/b` `[therefore sin^(2)theta+ cos^(2)theta=1 rArr costheta=sqrt(1-sin^(2)theta)]`
`therefore costheta=sqrt(1-sin^(2)theta)`
`=sqrt(1-(a/b)^(2)) = sqrt(1-a^(2)/b^(2))= (sqrtb^(2)-a^(2))/b`