Question

Find the value of `sin[2cot^-1 ((-5)/12)]`

Answer 1

Let `cot^-1 ((-5)/12)` = y.

Then cot y = `(-5)/12`

Now `sin[2cot^-1 ((-5)/12)]` = sin 2y

= 2siny cosy

= `2(12/13)((-5)/13)`  ......`["since" cot y < 0, "so"  y ∈(pi/2, pi)]`

= `(-120)/169`