If the angle `theta` is acute, then the acute angle between `x^(2)(cos theta-sin theta)+2xy cos theta+y^(2)(cos theta+sin theta)=0,` is

Options

A. `2 theta`
B. `theta//3`
C. `theta`
D. `theta//2`

Answer

C

Explanation

Here, `a=cos theta-sin theta, b=cos theta+sin theta and h=cos theta`.
Let `alpha` be the acute angle between the lines represented by the given equation. Then,
`tan alpha|(2sqrth^(2)-ab)/(a+b)|`
`rArr" "tan alpha=|(2sqrt(cos^(2)theta-(cos^(2)theta-sin^(2)sin^(2)theta)))/(2 cos theta)|=tan theta rArr alpha = theta`