`sin(135 - 30), sin(135) - sin(30)` Find the exact value of the expression.

`sin(135^0 - 30^0) = sin 135^0* cos 30^0 - cos 135^0 * sin 30^0 `

(we know that

`= sin (90+45) * cos 30 - cos(90+45) *sin 30^0 `

 `=cos 45^0 * cos 30 - (-sin 45^0) * sin 30^0`

`= 1/sqrt2 * sqrt3/2 +1/sqrt2 * 1/2...

`sin(135^0 - 30^0) = sin 135^0* cos 30^0 - cos 135^0 * sin 30^0 `

(we know that

`= sin (90+45) * cos 30 - cos(90+45) *sin 30^0 `

 `=cos 45^0 * cos 30 - (-sin 45^0) * sin 30^0`

`= 1/sqrt2 * sqrt3/2 +1/sqrt2 * 1/2 `

`= (sqrt3+1)/(2sqrt2) = 0.9661 `

lets check with direct values. `sin(105^0) = 0.9659 ~~ 0.966` ``

Next expression is

`sin(135^0) - sin (30^0) `

`sin(135^0) - sin (30^0) = sin(90^0 +45^0) - sin 30^0 `

                                       ` = cos 45^0 - sin30^0`

                                        `= 0.2071`