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Some Applications Of Trigonometry

Question
CBSEENMA10007657

If tan left parenthesis straight A plus straight B right parenthesis space equals square root of 3 space space and space tan left parenthesis straight A minus straight B right parenthesis space equals space fraction numerator 1 over denominator square root of 3 end fraction semicolon 0 degree less than straight A plus straight B less or equal than 90 degree semicolon space space space straight A greater than straight B. Find A and B.

Solution
tan left parenthesis straight A plus straight B right parenthesis space equals space square root of 3
⇒A + B = 60° ...(i)
and
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⇒A-B = 30° ...(ii)
Solving (i) and (ii), we get
A = 45° and B = 15°.