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| 1. |
If sin(A+B)=1 and cos(A+B)=^3/4,find A and B |
| Answer» sin (A + B) = 1\xa0{tex}\\Rightarrow{/tex}sin (A + B) = sin 90°{tex}\\Rightarrow A + B = 90 ^ { \\circ }{/tex}.......(i)cos (A - B) =\xa0{tex}\\frac { \\sqrt { 3 } } { 2 }{/tex}{tex}\\Rightarrow \\cos ( A - B ) = \\cos 30 ^ { \\circ }{/tex}{tex}\\Rightarrow A - B = 30 ^ { \\circ }{/tex}........(ii)Solving (i) and (ii), we get A =\xa060° and B = 30°.Hence, A = 60° and B = 30°. | |