Question

Find the value of cos5π/12?

Answer 1

`1/4(sqrt6-sqrt2)`

Explanation:

`"using the "color(blue)"trigonometric identity"`

`•color(white)(x)cos(x+y)=cosxcosy-sinxsiny`

`"note that "(5pi)/12=pi/6+pi/4`

`cos((5pi)/12)=cos(pi/6+pi/4)`

`=cos(pi/6)cos(pi/4)-sin(pi/6)sinpi(/4)`

`=(sqrt3/2xxsqrt2/2)-(1/2xxsqrt2/2)`

`=sqrt6/4-sqrt2/4=1/4(sqrt6-sqrt2)`