Question

How do you find the value of `sin (pi/3-pi/4)`?

Answer 1

`(sqrt3 - 1 )/(2sqrt2)`

Explanation:

Using appropriate`color(blue)" Addition formula "`

`• sin(A ± B ) = sinAcosB ± cosAsinB`

`sin(pi/3 - pi/4 ) = sin(pi/3)cos(pi/4) - cos(pi/3)sin(pi/4)`

and using `color(red) " exact values "`

`= sqrt3/2 . 1/sqrt2 - 1/2 . 1/sqrt2`

common denominator of `2sqrt2 " to obtain "`

`sin(pi/3 - pi/4 ) = (sqrt3 - 1)/(2sqrt2)`