Given that p = `tanalpha+tanbeta, andq=cotalpha+cotbeta`, then what is `((1)/(p)-(1)/(q))`equal to ?

Options

A. `cot(alpha-beta)`
B. `tan(alpha-beta)`
C. `tan(alpha+beta)`
D. `cot(alpha+beta)`

Answer

D

Explanation

Since , `p=tanalpha+tanbeta` and `q=cot alpha+cotbeta`
`q=cotalpha+cotbeta`
`rArrq=(1)/(tanalpha)+(1)/(tanbeta)=(tanalpha+tanbeta)/(tanalphatanbeta)`
`q=(p)/(tanalphatanbeta)rArr(1)/(q)=(tanalphatanbeta)/(p)`
Hence , `(1)/(p)-(1)/(q)=(1)/(p)-(tanalphatanbeta)/(p)`
`=(1-tanalphatanbeta)/(p)=(1-tanalphatanbeta)/(tanalpha+tanbeta)=(1)/(tan(alpha+beta))`
`=cot(alpha+beta)`