If tanθ =21 and tanϕ =31, then tan(2θ+ϕ ) is equal to

Given, tanθ =21;tanϕ =31∵tan2θ =1−tan2θ 2tanθ =1−41 2×21 =34Now, tan(2θ+ϕ)=1−tan2θ tanϕ tan2θ +tanϕ =1−34×31 34+31 =3

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If { } = { 1 }{ 2 } and { } = { 1 }{ 3 } , then { ( 2 +

Question

If $tan θ = \frac{1}{2}$ and $tan ϕ = \frac{1}{3}$ , then $tan (2 θ + ϕ)$ is equal to

\frac{3}{4}

\frac{4}{3}

\frac{1}{3}

\frac{1}{2}

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Chloe Discussed

tan θ = \frac{1}{2}

and

tan ϕ = \frac{1}{3}

, then

tan (2 θ + ϕ)

is equal to

10 mins ago

Discuss this question LIVE

10 mins ago

Given,

tan θ = \frac{1}{2}; tan ϕ = \frac{1}{3}

∵ tan 2 θ = \frac{2 tan θ}{1 - tan ^{2} θ}

= \frac{2 \times \frac{1}{2}}{1 - \frac{1}{4}} = \frac{4}{3}

Now,

tan (2 θ + ϕ) = \frac{tan 2 θ + tan ϕ}{1 - tan 2 θ tan ϕ}

= \frac{\frac{4}{3} + \frac{1}{3}}{1 - \frac{4}{3} \times \frac{1}{3}} = 3

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Question Text	If $tan θ = \frac{1}{2}$ and $tan ϕ = \frac{1}{3}$ , then $tan (2 θ + ϕ)$ is equal to
Answer Type	Text solution:1
Upvotes	150