Question

If Sin A + B equals to root 3 upon 2 and Cos A minus b equals to 1 where is zero degree less than a + b less than 90 degree and A is greater than or equal to b then find a and b.

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Answer 1

Answer:

A=30degrees,B=30degrees

Step-by-step explanation:

Answer 2

Answer:

The value of A = 30° and The value of B = 30°

Step-by-step explanation:

• Step-1:     Sin(A+B) = √3/2

                    ⇒ Sin(A+B) = Sin60°            [ As we know Sin60° = √3/2]

                    ⇒ (A+B) = 60°...........................(1)

• Step-2:     Cos(A-B) = 1

                    ⇒ Cos(A-B) = Cos0°             [ As we know Cos0° = 1]

                    ⇒ (A+B) = 0°...........................(2)

• Step-3:     From equation (1) and (2) we get

                           A +  B = 60  and A - B = 0

              By adding these two equation,   (A +  B) + (A - B) = 60 + 0

                                                                 ⇒ A + B + A - B = 60

                                                                 ⇒ 2A = 60

                                                                 ⇒ A = 60/2 = 30

        ∴  The value of A = 30°

• Step-4:     Substituting the value of A in equation (1)  we get

                           30 +  B = 60

                        ⇒ B = 60 -30 = 30

           ∴  The value of B = 30°

• Conclusion: A + B = 30 + 30 = 60° which is less than 90°.

                             and A = B .

           ∴ Both the conditions are satisfied.