What is the distance between the points (a cos 25, 0) and (0, a cos 65)?

Question

If
P=Sin A.Sin B,
Q= Sin C.Cos A,
R = Sin A.Cos B and
S=Cos A.Cos C
then
5(P^2+Q^2+R^2+S^2) = ??

Answer 1

Just apply the distance formula for points (a cos⁡〖25°,0〗 ) and (0,a cos⁡〖65°〗 )

= √([(a Cos25-0)^2+(0-a COs65)^2 ] )
= √([a^2 Cos^2 25+a^2 Cos^2 65] )

(When we take a^2 and taking it out of the root, it will give a)

a×√((Cos^2 25+Cos^2 65) )

(We know that by complimentary angles, Cos25=Sin65, SimilarlyCos^2 25=Sin^2 65)
a×√((Sin^2 65+Cos^2 65) )
(We know thatSin^2 X+Cos^2 X=1)
a×√((1) )
√1=1
a×1=a