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What will be the value of sec4 θ - tan4 θ, if sec2 θ + tan2 θ = 7/12?
  • a)
    1/2
  • b)
    7/12
  • c)
    1
  • d)
    2/3
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
What will be the value of sec4θ - tan4θ, if sec2θ + ...
Given sec2 θ + tan2 θ = 7/12
Now, here we can apply the formula -
a4 - b4 = (a2 - b2) (a2 + b2)
sec4 θ - tan4 θ = (sec2 θ - tan2 θ) (sec2 θ + tan2 θ)
= 1 x (sec2 θ + tan2 θ) {because 1 + tan2 θ = sec2 θ}
= 1 x 7/12
= 7/12
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Most Upvoted Answer
What will be the value of sec4θ - tan4θ, if sec2θ + ...

Given Information:

- sec2θ + tan2θ = 7/12

Calculation:

- We know the trigonometric identity sec2θ - tan2θ = 1.
- Therefore, sec2θ = tan2θ + 1
- Given sec2θ + tan2θ = 7/12
- Substituting sec2θ = tan2θ + 1, we get:
- tan2θ + 1 + tan2θ = 7/12
- 2tan2θ = 7/12 - 1
- 2tan2θ = 7/12 - 12/12
- 2tan2θ = -5/12
- tan2θ = -5/24

- Now, we need to find sec4θ - tan4θ. Using double angle identities:
- sec4θ - tan4θ = (sec2θ + tan2θ)(sec2θ - tan2θ)
- Substituting the values we have:
- sec4θ - tan4θ = (7/12)(1)
- sec4θ - tan4θ = 7/12

Therefore, the value of sec4θ - tan4θ is 7/12, which corresponds to option (b).
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Community Answer
What will be the value of sec4θ - tan4θ, if sec2θ + ...
Given sec2 θ + tan2 θ = 7/12
Now, here we can apply the formula -
a4 - b4 = (a2 - b2) (a2 + b2)
sec4 θ - tan4 θ = (sec2 θ - tan2 θ) (sec2 θ + tan2 θ)
= 1 x (sec2 θ + tan2 θ) {because 1 + tan2 θ = sec2 θ}
= 1 x 7/12
= 7/12
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What will be the value of sec4θ - tan4θ, if sec2θ + tan2θ = 7/12?a)1/2b)7/12c)1d)2/3Correct answer is option 'B'. Can you explain this answer?
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