Question

If 2cos (A+B)=2sin (A-B)=1
Find A and B

Answer 1

Hi ,

It is given that ,

2cos(A+ B ) = 2sin( A - B ) = 1

i ) 2cos( A + B ) = 1

Cos( A + B ) = 1/2

Cos( A + B ) = cos 60°

A + B = 60° ---( 1 )

ii ) 2sin( A - B ) = 1

Sin( A - B ) = 1/2

Sin( A - B ) = sin30°

A - B = 30 ----( 2 )

Add equations ( 1 ) and ( 2 ) we get,

2A = 90°

A = 90/2

A = 45°

Put A = 45° in equation ( 1 ) , we get

45° + B = 60°

B = 60 - 45

B = 15°

Therefore ,

A = 45° ,

B = 15°

I hope this helps you.

: )

Answer 2

Hi,

Please see the attached file!


Thanks