Question

How do you evaluate `Sin((5pi)/12) cos(pi/4) - cos((5pi)/12) sin(pi/4)`?

Answer 1

`0.5`

Explanation:

To evaluate `sin((5pi)/12)cos(pi/4)−cos((5pi)/12)sin(pi/4)`, we can use the identity

`sin(x-y)=sinxcosy-cosxsiny`

Hence `sin((5pi)/12)cos(pi/4)−cos((5pi)/12)sin(pi/4)`

= `sin((5pi)/12-pi/4) = sin((5pi)/12-(3pi)/12)` or

= `sin((2pi)/12)=sin(pi/6)=0.5`

Answer 2

`sin (pi/6) = 1/2`

Explanation:

Trig identity: sin (a - b) = sin a.cos b - sin b.cos a.
Therefor, the expression is reduced to:
`sin ((5pi)/12 - sin (pi/4)) = sin ((2pi)/12) = sin (pi/6) = 1/2`