Given that for a, b, c, d R , if a (200^ )-c (200^ )=d and b (200^ )+d (200^ )=c then a^2+b^2+c^2+d^2 a c-b d =p cosec (200^ ) find the value of p

Step-by-step solution

aligned & a (200^ ) - c (200^ ) (200^ ) =d ....(i) & b (200^ ) + d (200^ ) (200^ ) =c ....(ii) & a=d (200^ )+c (200^ ) .....(iii) & b=c (200^ )-d (200^ ) ....(iv) & a^2+b^2=c^2+d^2 & (a^2+b^2+c^2+d^2 )=2 (c^2+d^2 ) & a c=d c (200^ )+c^2 (200^ ) aligned b d= cd (200^ )-d^2 (200^ )Also, a c-b d= (c^2+d^2 ) (200^ ) aligned & So a^2+b^2+c^2+d^2 a c-b d = 2 (c^2+d^2 ) (c^2+d^2 ) (200^ ) =2 cosec (200^ ) & p=2 aligned