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Some Applications Of Trigonometry

Question
CBSEENMA10007937

If sin thin space left parenthesis straight A minus straight B right parenthesis space equals space 1 half comma space space space space space cos space left parenthesis straight A plus straight B right parenthesis space equals space 1 half comma space space space 0 degree less than straight A plus straight B less or equal than 90 degree comma space space straight A greater than straight B. Find A and B.

Solution

sin (A-B) = 1 half
rightwards double arrow          straight A minus straight B space equals space 30 degree             ...(i)
      cos left parenthesis straight A plus straight B right parenthesis space equals space 1 half
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#6 {main}</pre>            ...(ii)   
Solving (i) and (ii), we get
                     straight A equals 45 degree space and space straight B space equals space 15 degree.