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If Tan4θ + Tan2θ = 1, then what is the value of Cos4θ + Cos2θ?
  • a)
    8
  • b)
    10
  • c)
    1
  • d)
    2
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If Tan4θ + Tan2θ = 1, then what is the value of Cos4&theta...
Given:
Tan4θ + Tan2θ = 1
Formula:
Sec2θ - Tan2θ = 1
Sin2θ + Cos2θ = 1
Calculation:
Tan4θ + Tan2θ = 1
⇒ Tan2θ (Tan2θ + 1) = 1
⇒ Tan2θ. Sec2θ = 1      {∵ sec2θ = 1 + tan2θ}
⇒ (sin2 θ/cos4 θ) = 1
⇒ 1 – cos2θ = cos4 θ      {∵ sin2 θ = 1 – cos2θ}
⇒ cos4 θ + cos2 θ = 1
∴ Then the value of cos4 θ + cos2 θ is 1.
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Most Upvoted Answer
If Tan4θ + Tan2θ = 1, then what is the value of Cos4&theta...
Given:
Tan4θ + Tan2θ = 1
Formula:
Sec2θ - Tan2θ = 1
Sin2θ + Cos2θ = 1
Calculation:
Tan4θ + Tan2θ = 1
⇒ Tan2θ (Tan2θ + 1) = 1
⇒ Tan2θ. Sec2θ = 1      {∵ sec2θ = 1 + tan2θ}
⇒ (sin2 θ/cos4 θ) = 1
⇒ 1 – cos2θ = cos4 θ      {∵ sin2 θ = 1 – cos2θ}
⇒ cos4 θ + cos2 θ = 1
∴ Then the value of cos4 θ + cos2 θ is 1.
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If Tan4θ + Tan2θ = 1, then what is the value of Cos4θ + Cos2θ?a)8b)10c)1d)2Correct answer is option 'C'. Can you explain this answer?
Question Description
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