if `tantheta=1` then the value of `(8sintheta+5costheta)/(sin^(3)theta-2cos^(3)theta+7costheta)` is

Options

A. 2
B. `2(1)/(2)`
C. 3
D. `(4)/(3)`

Answer

a

Explanation

If, `tan theta=1`
It means `theta=45^(@)`
`=(sin theta+5cos theta)/(sin^(2)theta-2cos^(2)theta+7cos theta)`
`=(5sin45 ^(@)+5cos45^(@))/(sin^(2)45^(@)-2cos^(3)45^(@)+7cos45^(@))`
`(8xx(1)/sqrt(2)+5xx(1)/sqrt(2))/(((1)/sqrt(2))^(3)-((1)/sqrt(2))^(3)+7((1)/sqrt(2)))=2`