If sinθsinϕ2=tanθtanϕ=3 then which of the following is not true.
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a
tanϕ=13
b
tanϕ=−13
c
tanθ=3
d
tanθ=13
answer is D.
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Detailed Solution
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