Question

If A and B are angles of the right angled triangle ABC, right angled at C , prove that sin^2A +sin^2B=1

Answer 1

In triangle ABC
C=90
sin a=opp/hyp
Sin^2 A=BC^2/AB^2
Sin^2 B=AC^2/AB^2
SIN^2 A+ SIN^2 B =BC^2+AC^2/AB^2......1

By pythagoras theorem,
here,
BC^2 + AC^2=AB^2
SO
from 1
=AB^2/AB^2
=1
Hence proved