If tanα=x+1x and tanβ=2x+11,then α+β is -

We know, tan(α+β) =1−tanα.tanβtanα+tanβ=(2x+1)(x+1)−xx(2x+1)+x+1=2x2+2x+x+1−x2x2+2x+1=2x2+2x+12x2+2x+1=1Hence, α+β=4π

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If {}={x}{x+1} and {}={1}{2x+1},then + is -

Question

If $tan α = \frac{x}{x + 1}$ and $tan β = \frac{1}{2 x + 1}$ ,then $α + β$ is -

\frac{π}{4}

\frac{π}{3}

\frac{π}{2}

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Lucas Discussed

tan α = \frac{x}{x + 1}

and

tan β = \frac{1}{2 x + 1}

,then

α + β

is -

8 mins ago

Discuss this question LIVE

8 mins ago

We know,

tan (α + β)

= \frac{tan α + tan β}{1 - tan α . tan β}

= \frac{x ( 2 x + 1 ) + x + 1}{( 2 x + 1 ) ( x + 1 ) - x}

= \frac{2 x ^{2} + 2 x + 1}{2 x ^{2} + 2 x + x + 1 - x}

= \frac{2 x ^{2} + 2 x + 1}{2 x ^{2} + 2 x + 1}

= 1

Hence,

α + β = \frac{π}{4}

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Question Text	If $tan α = \frac{x}{x + 1}$ and $tan β = \frac{1}{2 x + 1}$ ,then $α + β$ is -
Answer Type	Text solution:1
Upvotes	150