If Sin(A+B) =V3/2=Cos (A-B),
0°<A+B<90° (A>B),
Find the value of A and B.​

Question

If Sin(A+B) =V3/2=Cos (A-B),
0°<A+B<90° (A>B),
Find the value of A and B.​

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Amaya 2 years 2021-06-22T02:31:28+00:00 1 Answers 0 views 0

Answers ( )

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    2021-06-22T02:33:25+00:00

    \bold\red{\fbox{\sf{Solution}}}

    sin(A+B)=cos(A-B)=√3/2

    ∴, sin(A+B)=√3/2

    or, sin(A+B)=sin60°

    or, A+B=60° –(1)

    cos(A-B)=√3/2

    or, cos(A-B)=cos30°

    or, A-B=30° –(2)

    Adding (1) and (2) we get,

    2A=90°

    or, A=45°

    Putting in (1) we get, 

    45°+B=60°

    or, B=15°

    ∴, A=45°, B=15°

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