Question

Sin-1 5/13+sin-1 16/65= = cos-1 4/5

Answer 1

Answer:

Step-by-step explanation:

L.H.S.=sin−1(45)+sin−1(513)+sin−1(1665)  

=sin−1(451−(513)2−−−−−−−−−√+5131−(45)2−−−−−−−−−√)+sin−1(1665)

=sin−1(45⋅1213+513⋅35)+sin−1(1665)

=sin−1(4865+1565)+sin−1(1665)

=sin−1(6365)+sin−1(1665)

=sin−1(63651−(1665)2−−−−−−−−−√+16651−(6365)2−−−−−−−−−√)

=sin−1(6365⋅6365+1665⋅1665)

=sin−1(652652)

=sin−1(1)=π2=R.H.S.