Question

sin (A+B) = 1 and cos (A-B)=root3 /2 then find the value of A and B
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Answer 1

Answer:

Required value of A is 60° and B is 30°.

Step-by-step explanation:

Given,

sin( A + B ) = 1

cos( A - B ) = √3 / 2

From the properties of trigonometry :

• sin90° = 1
• cos30° = √3 / 2

Therefore,

= > sin( A + B ) = 1

= > sin( A + B ) = sin90°

= > A + B = 90° ... ( 1 )

Also,

= > cos( A - B ) = √3 / 2

= > cos( A - B ) = cos30°

= > A - B = 30° ...( 2 )

Adding ( 1 ) and ( 2 ) :

= > ( A + B ) + ( A - B ) = 90° + 30°

= > A + B + A - B = 120°

= > 2A = 120°

= > A = 60°

Substituting the value of A in ( 1 ) :

= > A + B = 90°

= > 60° + B = 90°

= > B = 90° - 60°

= > B = 30°

Thus the required value of A is 60° and B is 30°.