Question

If `2tanbeta+cotbeta=tanalpha` , prove that `cotbeta=2tan(alpha-beta)dot`

Answer 1

`R.H.S. = 2tan(alpha-beta) = (2(tanalpha - tanbeta))/(1+tanalphatanbeta)`
`=(2(2tanbeta+cotbeta- tanbeta))/(1+(2tanbeta+cotbeta)tanbeta)`
`=(2(tanbeta+cotbeta))/(1+(2tan^2beta+cotbetatanbeta)`
`=(2(tanbeta+1/tanbeta))/(1+(2tan^2beta+1/tanbetatanbeta)`
`=(2((tan^2beta+1)/tanbeta))/(2(tan^2beta+1))`
`=1/tanbeta = cotbeta = L.H.S.`