If sin ⁡x=12 x = 1 2 , and 0<x<π2 0 < x < π 2 , what is cos⁡(x−π6) ( x − π 6 ) ?

Answer 1

Do you mean sinx = 1/2? If so, then cosx = √ [1 - sin²x] = √3/2.

So, cos(x - π/6) = cosxcosπ/6 + sinxsinπ/6 = (√3/2)(√3/2) + (1/2)(1/2) = 1

Answer 2

Please rewrite the problem. ^ is power.