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If : =a 0, : 2 =b 0 and : +: 2 =: 3 then

Question

If $tan θ = a \neq = 0, tan 2 θ = b \neq = 0$ and $tan θ + tan 2 θ = tan 3 θ$ then

A

a = b

B

ab = 1

C

a + b = 0

D

b = 2 a

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Chloe Discussed

If

tan θ = a \neq = 0, tan 2 θ = b \neq = 0

and

tan θ + tan 2 θ = tan 3 θ

then

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

a = tan θ & b = tan 2 θ

where

a \neq = 0, b \neq = 0

...(1)

tan θ + tan 2 θ = tan 3 θ

...(2)

A - B = C tan (A - B) = tan C

\Rightarrow \frac{tan A - tan B}{1 + tan A tan B} = tan C

\Rightarrow tan A - tan B - tan C = tan A tan B tan C

\Rightarrow tan 3 θ - tan 2 θ - tan θ = tan 3 θ tan 2 θ tan θ

\Rightarrow ab tan 3 θ = 0

...{ from (2)}

∵ a \neq = 0, b \neq = 0 ∴ tan 3 θ = 0 \Rightarrow tan θ + tan 2 θ = 0

\Rightarrow a + b = 0

...{ from (1)}

Ans: C

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Question Text	If $tan θ = a \neq = 0, tan 2 θ = b \neq = 0$ and $tan θ + tan 2 θ = tan 3 θ$ then
Answer Type	Text solution:1
Upvotes	150