Question

if tanA+tanB=x and cotA+cotB=y then prove that, cot(A+B)=(1/x - 1/y)

Answer 1

hi, have you attempted it by yourself first ?

and know the formula for tan(A+B) or cot (A+B ) ?

Answer 2

\[\cot(A+B) = \frac{1-\tan A \tan B}{\tan A + \tan B} = \frac{1}{x} - \frac{\frac{1}{\cot A \cot B}}{\frac{1}{\cot A} +\frac{1}{\cot B}}\]
can you take it from there

Answer 3

if you're comfortable with tan (A+B) formula,
then
write
cot A + cot B = y in terms of tan,
to get
x/(tan A tan B) = y

now you have
tan A tan B and tan A + tan B in terms of x and y
just rearrange