Which one of the following is a value of θ, if θ satisfies the equation tan 2θ tan 4θ - 1 = 0;  ?

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CDS Elementary Mathematics 3 Sep 2023 Official Paper
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Answer (Detailed Solution Below)

Option 1 :
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Detailed Solution

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Given:

tan 2θ tan 4θ - 1 = 0, 

Concept Used:

If tan A + tan B = 1

Then A + B = 900

Calculation:

According to the question

⇒ tan 2θ tan 4θ - 1 = 0

⇒ tan 2θ tan 4θ = 1

⇒ 2θ + 4θ = 900

⇒ θ = 150

∴ The value of θ is  which satisfies the equation tan 2θ tan 4θ - 1 = 0.

Alternate Method We have to check for which value of θ, 

The equation tan 2θ tan 4θ - 1 = 0 satisfies

Option (1): θ =  = 150

⇒ tan 2θ tan 4θ - 1 = tan 2(150) tan 4(150) - 1

⇒ tan 2θ tan 4θ - 1 = tan 300 tan 600 - 1

⇒ tan 2θ tan 4θ - 1 = (× √3) - 1 = 0

∴ The value of θ is  which satisfies the equation tan 2θ tan 4θ - 1 = 0.

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