Question:
Prove that tan^-1 2/11 + tan^-1 2/11+ tan^-1 7/24 =tan^-1 1/2.
Answer:
Correct question is:
Prove that tan-1 (2/11) + tan-1 (7/24) = tan-1 (1/2)
Solution:
GIven, tan-1 (2/11) + tan-1 (7/24)
= tan-1 {2/11 + 7/24)/(1 - 2/11 * 7/24)}
= tan-1 [{(2*24 + 7*11)(11*24)}/{(11*24 - 2*7)/(11*24)}]
= tan-1 {(2*24 + 7*11)/(11*24 - 2*7)}
= tan-1 {(48 + 77)/(264 - 14)}
= tan-1 (125/250)
= tan-1 (1/2)
So, tan-1 (2/11) + tan-1 (7/24) = tan-1 (1/2)
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