Using the formula `cos (A+B) = cosA cosB -sin A sin B`. find the value of sin `15^(@)`.

Explanation

We can find the vlaue of cosine of an angle from the given formula . So first of all we will convert `sin15^(@)` into the cosine of some angle and then use the given formula .
`:. sin15^(@)=sin(90^(@)-75^(@))=cos75^(@)`
so , put `A=45^(@)andB=30^(@)` in the given formula,
`:.cos(45^(@)+30^(@))=cos45^(@)cos30^(@)-sin45^(@)sin30^(@)`
`rArrcos75^(@)=(1)/(sqrt(2))xx(sqrt(3))/(2)-(1)/(sqrt(2))xx(1)/(2)`
`rArrcos(90^(@)-15^(@))=(sqrt(3))/(2sqrt(2))-(1)/(2sqrt(2))`
`rArrsin15^(@)=(sqrt3-1)/(2sqrt(2))`