NIMCET 2013 Question Paper with solutions

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Question : 50 of 120

Marks: +1, -0

If tan α =

m/{m+1}

and tan β =

1/{2m+1}

then α + β is equal to :

π/3
π/4
π/6
π

Solution:

Given,

\tanα=m/{m+1}

and

\tanβ=1/{2m+1}

∴\tan(α+β)={\tanα+\tanβ}/{1-\tanα-\tanβ}

={{m}/{m+1}+{1}/{2m+1}}/{1-({m}/{m+1})({1}/{2m+1})}={2m^{2}+2m+1}/{2m^{2}+2m+1}=1

⇒\tan(α+β)=1

⇒α+β=π/4

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