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If tan alpha =m/(m+1) and tan beta =1/(2...

If `tan alpha =m/(m+1)` and `tan beta =1/(2m+1)` , then `alpha+beta` is equal to

A

`(pi)/(2)`

B

`(pi)/(3)`

C

`(pi)/(6)`

D

`(pi)/(4)`

Text Solution

Verified by Experts

Given that, `tanalpha=(m)/(m+1) and tanbeta=(1)/(2m+1)`
Now, `" "tan (alpha+beta)=(tanalpha+tanbeta)/(1-tanalpha*tanbeta)`
`rArr" "tan(alpha+beta)=((m)/(m+1)+(1)/(2m+1))/(1-((m)/(m+1))((1)/(2m+1)))`
`rArr" "tan(alpha+beta)=(m(2m+1)+m+1)/((m+1)(2m+1)-m)`
`rArr" "tan(alpha+beta)=(2m^(2)+m+m+1)/(2m^(2)+2m+m+1-m)`
`rArr" "tan(alpha+beta)=(2m^(2)+2m+1)/(2m^(2)+2m +1)rArrtan(alpha+beta)=1`
`therefore" "alpha+beta=(pi)/(4)`
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