Question

Find a formula for cot(x+y) in terms of cot(x) and cot(y)

Answer 1

\(\bf {\color{blue}{ tan(\theta+\beta)=\cfrac{tan(\theta)+tan(\beta)}{1-tan(\theta)tan(\beta)}\qquad \qquad tan(\alpha)=\cfrac{1}{cot(\alpha)}}}\\ \quad \\ \quad \\
cot(x+y)\implies \cfrac{1}{tan(x+y)}\implies \cfrac{1}{\frac{tan(x)+tan(y)}{1-tan(x)tan(y)}}\\ \quad \\
\cfrac{1-tan(x)tan(y)}{tan(x)+tan(y)}\)

now convert the tangent's to cotangents

Answer 2

thanks a lot :)

Answer 3

yw