cotangent

• October 2nd 2008, 01:48 AM
maeca
cotangent
Can I distribute cotangent here???

cot(Arccot 3 + Arccot 7 + Arccot 15 + Arccot 21)

Can you please show the solution???
• October 2nd 2008, 03:29 AM
bobak
Quote:

Originally Posted by maeca
Can I distribute cotangent here???

cot(Arccot 3 + Arccot 7 + Arccot 15 + Arccot 21)

Can you please show the solution???

nope you cannot distribute the cotangent here, you will need to use the double angle formula here (several times)

first note that $\cot ( A + B ) = \frac{\cot A \cot B - 1}{\cot A + \cot B}$

so your thing becomes

$\cot( accot 3 + acot 7 + acot 15 + acot 21) = \frac{\cot (accot 3 + acot 7) \cot (acot 15 + acot 21) - 1}{\cot (accot 3 + acot 7) + \cot (acot 15 + acot 21)}
$

can you finish this off ?

Bobak