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√p.p+ q.q= q sec theta
RHS
q sec + q)/ q sec - q
sec+ 1/ sec -1
( sec + 1)^2/ tan^2
LHS
q sec /p + q/p)^2
q( 1 + sec)/p)^2
q^2 ( 1 + sec)^2/p^2
AS √ p^2 + q^2 = q sec
p^2 + q^2 = q^2 sec^2
(p/q)^2 + 1 = sec^2
( p/q)^2 = sec^2 -1
substitute in q^2( 1+ sec)^2/ p^2
(sec +1)^2/ sec^2 -1
sec+1)^2/ tan^2 = RHS
RHS
q sec + q)/ q sec - q
sec+ 1/ sec -1
( sec + 1)^2/ tan^2
LHS
q sec /p + q/p)^2
q( 1 + sec)/p)^2
q^2 ( 1 + sec)^2/p^2
AS √ p^2 + q^2 = q sec
p^2 + q^2 = q^2 sec^2
(p/q)^2 + 1 = sec^2
( p/q)^2 = sec^2 -1
substitute in q^2( 1+ sec)^2/ p^2
(sec +1)^2/ sec^2 -1
sec+1)^2/ tan^2 = RHS
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