Question

if a triangle with sides 12 unit and 5 unit is inscribed in a circle with BC as diameter, then find the value of sin square theta +cos square theta -1

Answer 1

Is this supposed to be a trick question?

sin^2 Ø + cos^2 Ø - 1
= 1 - 1
= 0

the fact that we have a triangle of sides 12 and 5 in a circle has nothing to do with it.

Answer 2

btw, as an aside to your question ...

Any angle subtended by a diameter is a right-angle, so you would have the 5-12-13 right-angled triangle.
the larger of the acute angles is arctan(12/5)
and the smaller is arctan(5/12) ---> appr 22.6°

note:
sin^2 22.6° + cos^2 22.6° - 1
= 1-1 = 0