If `abs(cos theta{sin theta+sqrt(sin^2theta+sin^2alpha)})lek`, then the value of k

Options

A. `sqrt(1+cos^2alpha)`
B. `sqrt(1+sin^2alpha)`
C. `sqrt(2+sin^2alpha)`
D. `sqrt(2+cos^2alpha)`

Answer

B

Explanation

Let `u=costheta{sintheta+sqrt(sin^2theta+sin^2alpha}`
`or (u-sinthetacostheta)^2=cos^2theta(sin^2theta+sin^2alpha)`
`or u^2tan^2theta-2utantheta+u^2-sin^2alpha=0`
Since `tantheta` is real, we have
`4u^2-4u^2(u^2-sin^2LPH)ge0`
`or u^2le1+sin^2alpha`
`or absulesqrt(1+sin^2alpha)`