Question

if sin (A-B)=1/2,cos(A+B)=1/2,0°<A+B<90°,A>B,find AandB
plz ans this
the correct ans is A=45°
B=15°​

Answer 1

Step-by-step explanation:

sin(A-B) =1/2

sin(A-B) =sin 30 (bcause 1/2=30)

A-B=30---------------------1

cos(A+B) = 1/2

cos (A+B) =cos 60

A+B = 60-------------------2

Adding 1 and 2 we get 2A = 90

A = 90/2

A= 45

substituting A=45 in 1

A-B = 30

45-B=30

-B=30-45

-B=-15

B=15

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Answer 2

cos(A+B) = 1/2

=> cos(A+B) = cos(60) [0<A+B<90]

=> A + B = 60

sin(A-B) = 1/2

=> sin(A-B) = sin(30) or sin(150)

=> A - B = 30 or 150

Situation 1:-

A - B = 30

A + B = 60

on solving we get A = 45 and B = 15

Situation 2:-

A - B = 150

A + B = 60

on solving we get A = 105 B = - 45

Value of A can Either be 45 or 105

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