Question

if root )3 tan(theta)=3 sin(teta) then prove theat sin^2(teta)-cos^2(teta)=1/3

Answer 1

so ya here is ur answer
tan∅/sin∅=3/√3
opp/adj*hypo/opp=3/√3
hypo/adj=sec∅=3/√3
according to pythagoras theorem
the opp side will be √6
(since i am dng in laptop i cannot insert pictures)
LHS=sin2∅-cos2∅
=(√6/3)2-(√3/3)2
=6/9-3/9
=3/9=1/3
RHS=1/3
therefore LHS=RHS
thus sum proved