Home
Class 11
MATHS
If alphaa n dbeta are acute angles such ...

If `alphaa n dbeta` are acute angles such that `t a nalpha=m/(m+1)a n dt a nbeta=1/(2m+1)` , prove that `alpha+beta=pi/4` .

Text Solution

Verified by Experts

`tan(A+B)=(tanA+tanB)/(1-tanAtanB)`
`=(m/(m+1)+1/(2m+1))/(1-m/(m+1).1/(2m+1))`
`=((m(2m+1)+(m+1))/((m+1)(2m+1)))/(((m+1)(2m+1)-m)/((m+1)(2m+1)))`
`(2m^(2)+m+m+1)/(2m^(2)+2m+m+1-m)`
`=(2m^(2)+2m+1)/(2m^(2)+2m+1)=1=tanpi/4`
`therefore A+B=pi/4`. Hence Proved.
Promotional Banner

Topper's Solved these Questions

  • TRIGNOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN|Exercise EXERCISES 3A|11 Videos

  • TRIGNOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN|Exercise EXERCISES 3B|22 Videos

  • STRAIGHT LINES

    NAGEEN PRAKASHAN|Exercise Exercise|206 Videos

Similar Questions

Explore conceptually related problems

If alpha and beta are acute angles such that tan alpha=(m)/(m+1) and tan beta=(1)/(2m+1), prove that alpha+beta=(pi)/(4)

lim alpha=(m)/(m+1),tan beta=(1)/(2m+1), prove that alpha+beta=(pi)/(4)

If tanalpha=(m)/(m+1)andtan beta=(1)/(2m+1) , then (alpha+beta)=?

If alpha and beta are acute angles and cot alpha=(1)/(4) and cot beta=(5)/(3)* prove that alpha-beta=45

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

If A,B are acute angles such that tan(alpha+beta)=1,tan(alpha-beta)=(1)/(sqrt(3)) then tan4 alpha

Given that tanalpha=m//(m+1),tanbeta=1//(2m+1) , then what is the value of alpha+beta ?