Question:
Show that sin-1 5/13 + cos-1 3/5 = tan-1 63/16
Solution:
Here, sin-1 5/13 = tan-1 5/12
And,
cos-1 3/5 = tan-1 4/3
Taking the L.H.S, we have
L.H.S. $=\sin ^{-1} \frac{5}{13}+\cos ^{-1} \frac{3}{5}$
$=\tan ^{-1} \frac{5}{12}+\tan ^{-1} \frac{4}{3}=\tan ^{-1} \frac{\frac{5}{12}+\frac{4}{3}}{1-\frac{5}{12} \cdot \frac{4}{3}}$
$=\tan ^{-1} \frac{\frac{15+48}{36}}{\frac{36-20}{36}}=\tan ^{-1} \frac{63}{16}$
Thus, L.H.S = R.H.S
– Hence Proved