We have to write 15 degree as the difference of two angles.
And
[tex] 15 = 45-30, 15=60-45 [/tex]
Now we have to use the formula of cotangent of a difference of those two angles.
And the formula is
[tex] cot( \alpha - \beta) = \frac{ cot \alpha cot \beta +1}{ cot \beta -cot \alpha } [/tex]
THerefore,[tex] cot(45-30) = \frac{ cot45 cot 30 +1}{cot 30 -cot 45}
\\
cot(60-45) = \frac{cot60 cot 45 +1}{cot 45-cot 60} [/tex]
And that's the required expressions .
