Given that for \( a, b, c, d \in R \). if \( a \sec \left(190^{\circ}\right)-c \tan \left(190^{\...

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Given that for \( a, b, c, d \in R \). if \( a \sec \left(190^{\circ}\right)-c \tan \left(190^{\circ}\right) \) \( =d \) and \( b \sec \left(190^{\circ}\right)+d \tan \left(190^{\circ}\right)=c \), then find the value of \( \left(\frac{a^{2}+b^{2}+c^{2}+d^{2}}{b d-a c}\right) \sin 10^{\circ} \)
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