Question

Evaluate :sin[2cot inverse (-5/12)]

Answer 1

let Ф = cot⁻¹ (-5/12)
cotФ = -5/12  ⇒ tanФ = -12/5
so, sinФ = +_ 12/13, when we let sine is in 2nd quadrant then sinФ = 12/13
     cosФ = -5/13

so, sin[2cot⁻¹(-5/12)] = sin2Ф
  = 2sinФ.cosФ
= 2(12/13)(-5/13)
= -120/169

hence, answer is -120/169