QJEEM22Ma443d: JEE Main 2022 Mathematics - Class 11 JEEM22Ma443d Solution: Let S = [ − π , π 2 ) − { − π 2 , − π 4 , − 3 π 4 , π 4 } .…

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QJEEM22Ma443d: JEE Main 2022 Mathematics - Class 11 JEEM22Ma443d Solution: Let S = [ − π , π 2 ) − { − π 2 , − π 4 , − 3 π 4 , π 4 } .…

Let $S = [- π, \frac{π}{2}) - {- \frac{π}{2}, - \frac{π}{4}, - \frac{3 π}{4}, \frac{π}{4}}$ . Then the number of elements in the set $∣ A = {θ \in S : \tan θ (1 + \sqrt{5} \tan (2 θ)) = \sqrt{5} - \tan (2 θ)}$ is __________.

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Accepted Answer

Let $\tan α = \sqrt{5}$

$∴$ $\tan θ = \frac{\tan α - \tan 2 θ}{1 + \tan α \tan 2 θ}$

$∴$ $\tan θ = \tan (α - 2 θ)$

$α - 2 θ = n π + θ$

$\Rightarrow 3 θ = α - n π$

$\Rightarrow θ = \frac{α}{3} - \frac{n π}{3}; n \in Z$

If $θ \in [- π, π / 2]$ then $n = 0, 1, 2, 3, 4$ are acceptable

$∴$ 5 solutions.

QJEEM22Ma443d: JEE Main 2022 Mathematics - Class 11 JEEM22Ma443d Solution: Let S = [ − π , π 2 ) − { − π 2 , − π 4 , − 3 π 4 , π 4 } .…

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