Prove, sin−1817+sin−135=tan−17736
LHS=sin−1(817)+sin−1(35)=sin−1[817√1−(35)2+35√1−(817)2][∴ sin−1x+sin−1y=sin−1(x√1−y2+y√1−x2)]=sin−1(817×45+35×1517)=sin−1(7785)=tan−1⎡⎢⎣7785√1−(7785)2⎤⎥⎦ (∵ sin−1x=tan−1x√1−x2)=tan−1[7785×8536]=tan−17736=RHS.
Prove that sin−1817+sin−135=sin−17785.