[tex]\mathsf {sin (A + B) = \frac{1}{\sqrt{2} }}[/tex]
[tex]\implies \mathsf {A + B = 45}[/tex]
[tex]\mathsf {sin (A - B) = \frac{1}{2}}[/tex]
[tex]\implies \mathsf {A - B = 30}[/tex]
[tex]\textsf {Now add both values (to find A) :}[/tex]
[tex]\implies \mathsf {2A = 75}[/tex]
[tex]\implies \mathsf {A = 37.5}[/tex]
[tex]\textsf {Substitute in previous equation to find B :}[/tex]
[tex]\implies \mathsf {37.5 + B = 45}[/tex]
[tex]\implies \mathsf {B = 7.5}[/tex]
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Answers & Comments
[tex]\mathsf {sin (A + B) = \frac{1}{\sqrt{2} }}[/tex]
[tex]\implies \mathsf {A + B = 45}[/tex]
[tex]\mathsf {sin (A - B) = \frac{1}{2}}[/tex]
[tex]\implies \mathsf {A - B = 30}[/tex]
[tex]\textsf {Now add both values (to find A) :}[/tex]
[tex]\implies \mathsf {2A = 75}[/tex]
[tex]\implies \mathsf {A = 37.5}[/tex]
[tex]\textsf {Substitute in previous equation to find B :}[/tex]
[tex]\implies \mathsf {37.5 + B = 45}[/tex]
[tex]\implies \mathsf {B = 7.5}[/tex]