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If ${(\frac{\sin θ}{\sin ϕ})}^{2} = \frac{\tan θ}{\tan ϕ} = 3 t h e n$ which of the following is not true.

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tanϕ=13

tanϕ=−13

tanθ=3

tanθ=13

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detailed solution

Correct option is D

We have sinθsinϕ2=tanθtanϕ=3⇒sinθsinϕ.sinθsinϕ=sinθsinϕ.cosϕcosθ⇒sin2θ=sin2ϕ⇒2tanθ1+tan2θ=2tanϕ1+tan2ϕ⇒6tanϕ1+9tan2ϕ=2tanϕ1+tan2ϕ ∵tanθ=3tanϕ ⇒tan2ϕ=13⇒ tanϕ=±13⇒ tanθ=±3

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If sinθsinϕ2=tanθtanϕ=3 then which of the following is not true.

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If ${(\frac{\sin θ}{\sin ϕ})}^{2} = \frac{\tan θ}{\tan ϕ} = 3 t h e n$ which of the following is not true.