Question

18. (a) Find A and B if sin (A - B)
1
2
cos(A + B) and A, B are acute angles.
3
(b) Find A and B if cos(A - B)
= sin(A + B) and A, B are acute angles whose sum is acute.
2​

Answer 1

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$\sf{sin(A+B)=cos(A-B) = \sqrt{\frac{3}{2}}} \\ \sf{∴ \: sin(A+B)=\sqrt{\frac{3}{2}}} \\ \sf{or, sin(A+B)=sin60°} \\ \sf{or, A+B=60° ----(1)} \\ \sf{cos(A-B)=\sqrt{\frac{3}{2}}} \\ \sf{or, cos(A-B)=cos30°} \\ \sf{or, A-B=30° -----(2)} \\ \sf{Adding (1) and (2) we get,} \\ \sf{2A=90°} \\ \sf{or, A=45°} \\ \sf{Putting \: in \: (1) \: we \: get, } \\ \sf{45°+B=60°} \\ \sf{or, B=15°} \\ \sf{∴, A=45°, B=15°}$

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