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Question

Write the value of tan-1ab-tan-1a-ba+b.


Solution

We know that tan-1x-tan-1y=tan-1x-y1+xy.
Now,
tan-1ab-tan-1a-ba+b=tan-1ab-a-ba+b1+aba-ba+b=tan-1a2+ab-ab+b2ba+bab+b2-ab+a2ba+b=tan-11=tan-1tanπ4      tanπ4=1=π4

∴ tan-1ab-tan-1a-ba+b=π4

Mathematics
RD Sharma XII Vol 1 (2015)
Standard XII

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