Question

11. If cos (A – B) =
$\frac{ \sqrt{3} }{2} \:$
and sin ( A +B ) = 1, then find the value of A and B.


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Answer 1

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We have

=> cos (A - B) = √3/2

We know cos30° = √3/2

Thus A - B = 30 ---------(1)

Similarly , sin(A + B) = 1

We know sin90° = 1

=> A + B = 90 -------------(2)

Add (1) and (2)

=> A - B + A + B = 30 + 90

=> 2A = 120

=> A = 60° <<<<<<< Answer

Similarly B = 30° <<<<< Answer

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Hope this helps ✌️

Answer 2

Given,

⇒ cos ( A - B ) = √3/2

We know that, cos 30° = √3/2,

⇒ cos 30° = √3/2

•°• ( A - B ) = 30° ----------- ( 1 )

And,

⇒ sin ( A + B ) = 1

We know that, sin 90° = 1

⇒ sin 90° = 1

•°• ( A + B ) = 90° ------------- ( 2 )

Adding ( 1 ) and ( 2 ),

⇒ A - B + A + B = 30° + 90°

⇒ 2A = 120°

⇒ A = 120° ÷ 2

•°• A = 60°

Putting the value of A = 60° in ( 1 ),

⇒ A - B = 30°

⇒ 60° - B = 30°

⇒ 60° - 30° = B

⇒ 30° = B

•°• B = 30°

Hence, A = 60° and B = 30°.