If the segments joining the points `A(a , b)a n d\ B(c , d)` subtends an angle `theta` at the origin, prove that : `cos theta=(a c+b d)/sqrt((a^2+b^2)(c^2+d^2))`

Explanation

We have to prove that `cos theta=(a c+b d)/sqrt((a^2+b^2)(c^2+d^2))`
Let slope of `OA=b/a`

And slope of `OB=d/c`

Then angle between OA and OB is

`tantheta=|(m_2-m_1)/(1+m_1m_2)|=|((d/c)-(b/c))/(1+((bd)/(ac)))|`

`tantheta=|(ad-bc)/(ac-bd)|=p/b`
Then,

`impliescostheta=b/h=|
(ac+bd)/(sqrt((ad-bc)^2+(ac+bd)^2))|`

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