Question

if sin(a+b)=√3/2=cos(a-b) find the value of a and b

Answer 1

Hi ,

It is given that ,

sin( a + b ) = √3/2 = cos( a - b )

i ) sin( a + b ) = √3/2

sin( a + b ) = sin 60°

a + b = 60 -----( 1 )

ii ) cos( a - b ) = √3/2

cos( a - b ) = cos 30°

a - b = 30 ---( 2 )

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

2a = 90

a = 90/2

a = 45°

substitute a = 45° in equation ( 1 ),

45° + b = 60°

b = 60° - 45°

b = 15°

Therefore ,

a = 45° , b = 15°

I hope this helps you.

: )