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If the value of tan2 θ + tan4 θ = 1, what will be the value of cos2 θ + cos4 θ?
- a)4
- b)1
- c)-2
- d)-1
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If the value of tan2 θ + tan4 θ = 1, what will be the valu...
Given, tan2 θ + tan4 θ = 1 …. (i)
From equation (i),
tan2 θ ( 1 + tan2 θ ) = 1
tan2 θ ( sec2 θ ) = 1 [As according to the trigonometric identity, sec2 θ - tan2 θ = 1]
tan2 θ = 1/ sec2 θ
tan2 θ = cos2 θ ….(ii)
Now, cos2 θ + cos4 θ = ?
⇒ cos2 θ + (cos2)2 θ
⇒ tan2 θ + (tan2)2 θ
⇒ tan2 θ + tan4 θ
= 1 {from equation (i)}
From equation (i),
tan2 θ ( 1 + tan2 θ ) = 1
tan2 θ ( sec2 θ ) = 1 [As according to the trigonometric identity, sec2 θ - tan2 θ = 1]
tan2 θ = 1/ sec2 θ
tan2 θ = cos2 θ ….(ii)
Now, cos2 θ + cos4 θ = ?
⇒ cos2 θ + (cos2)2 θ
⇒ tan2 θ + (tan2)2 θ
⇒ tan2 θ + tan4 θ
= 1 {from equation (i)}
Most Upvoted Answer
If the value of tan2 θ + tan4 θ = 1, what will be the valu...
Given, tan2 θ + tan4 θ = 1 …. (i)
From equation (i),
tan2 θ ( 1 + tan2 θ ) = 1
tan2 θ ( sec2 θ ) = 1 [As according to the trigonometric identity, sec2 θ - tan2 θ = 1]
tan2 θ = 1/ sec2 θ
tan2 θ = cos2 θ ….(ii)
Now, cos2 θ + cos4 θ = ?
⇒ cos2 θ + (cos2)2 θ
⇒ tan2 θ + (tan2)2 θ
⇒ tan2 θ + tan4 θ
= 1 {from equation (i)}
From equation (i),
tan2 θ ( 1 + tan2 θ ) = 1
tan2 θ ( sec2 θ ) = 1 [As according to the trigonometric identity, sec2 θ - tan2 θ = 1]
tan2 θ = 1/ sec2 θ
tan2 θ = cos2 θ ….(ii)
Now, cos2 θ + cos4 θ = ?
⇒ cos2 θ + (cos2)2 θ
⇒ tan2 θ + (tan2)2 θ
⇒ tan2 θ + tan4 θ
= 1 {from equation (i)}
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Community Answer
If the value of tan2 θ + tan4 θ = 1, what will be the valu...
Given, tan2 θ + tan4 θ = 1 …. (i)
From equation (i),
tan2 θ ( 1 + tan2 θ ) = 1
tan2 θ ( sec2 θ ) = 1 [As according to the trigonometric identity, sec2 θ - tan2 θ = 1]
tan2 θ = 1/ sec2 θ
tan2 θ = cos2 θ ….(ii)
Now, cos2 θ + cos4 θ = ?
⇒ cos2 θ + (cos2)2 θ
⇒ tan2 θ + (tan2)2 θ
⇒ tan2 θ + tan4 θ
= 1 {from equation (i)}
From equation (i),
tan2 θ ( 1 + tan2 θ ) = 1
tan2 θ ( sec2 θ ) = 1 [As according to the trigonometric identity, sec2 θ - tan2 θ = 1]
tan2 θ = 1/ sec2 θ
tan2 θ = cos2 θ ….(ii)
Now, cos2 θ + cos4 θ = ?
⇒ cos2 θ + (cos2)2 θ
⇒ tan2 θ + (tan2)2 θ
⇒ tan2 θ + tan4 θ
= 1 {from equation (i)}
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If the value of tan2 θ + tan4 θ = 1, what will be the value of cos2 θ + cos4 θ?a)4b)1c)-2d)-1Correct answer is option 'B'. Can you explain this answer?
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