Show that

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

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