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If tan θ + sec θ = 4, then find the value of cos θ ?
- a)5/17
- b)8/17
- c)11/17
- d)13/17
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If tan θ + sec θ = 4, then find the value of cos θ ?...
Concept:
I. sec2 θ – tan2 θ = 1
II. a2 – b2 = (a - b) (a + b)
I. sec2 θ – tan2 θ = 1
II. a2 – b2 = (a - b) (a + b)
Calculation:
Given:
tan θ + sec θ = 4 ...(1)
As we know that, sec2 θ – tan2 θ = 1
⇒ sec2 θ – tan2 θ = 1
⇒ (sec θ – tan θ) (sec θ + tan θ) = 1
By substituting the value of tan θ + sec θ = 4, in the above equation, we get
⇒ sec θ – tan θ = 1/4 ... (2)
Adding equation (1) and (2), we get
⇒ 2 sec θ = 17/4
⇒ sec θ = 17/8
cos θ = 8/17
Given:
tan θ + sec θ = 4 ...(1)
As we know that, sec2 θ – tan2 θ = 1
⇒ sec2 θ – tan2 θ = 1
⇒ (sec θ – tan θ) (sec θ + tan θ) = 1
By substituting the value of tan θ + sec θ = 4, in the above equation, we get
⇒ sec θ – tan θ = 1/4 ... (2)
Adding equation (1) and (2), we get
⇒ 2 sec θ = 17/4
⇒ sec θ = 17/8
cos θ = 8/17
Most Upvoted Answer
If tan θ + sec θ = 4, then find the value of cos θ ?...
Concept:
I. sec2 θ – tan2 θ = 1
II. a2 – b2 = (a - b) (a + b)
I. sec2 θ – tan2 θ = 1
II. a2 – b2 = (a - b) (a + b)
Calculation:
Given:
tan θ + sec θ = 4 ...(1)
As we know that, sec2 θ – tan2 θ = 1
⇒ sec2 θ – tan2 θ = 1
⇒ (sec θ – tan θ) (sec θ + tan θ) = 1
By substituting the value of tan θ + sec θ = 4, in the above equation, we get
⇒ sec θ – tan θ = 1/4 ... (2)
Adding equation (1) and (2), we get
⇒ 2 sec θ = 17/4
⇒ sec θ = 17/8
cos θ = 8/17
Given:
tan θ + sec θ = 4 ...(1)
As we know that, sec2 θ – tan2 θ = 1
⇒ sec2 θ – tan2 θ = 1
⇒ (sec θ – tan θ) (sec θ + tan θ) = 1
By substituting the value of tan θ + sec θ = 4, in the above equation, we get
⇒ sec θ – tan θ = 1/4 ... (2)
Adding equation (1) and (2), we get
⇒ 2 sec θ = 17/4
⇒ sec θ = 17/8
cos θ = 8/17
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If tan θ + sec θ = 4, then find the value of cos θ ?a)5/17b)8/17c)11/17d)13/17Correct answer is option 'B'. Can you explain this answer?
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If tan θ + sec θ = 4, then find the value of cos θ ?a)5/17b)8/17c)11/17d)13/17Correct answer is option 'B'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about If tan θ + sec θ = 4, then find the value of cos θ ?a)5/17b)8/17c)11/17d)13/17Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If tan θ + sec θ = 4, then find the value of cos θ ?a)5/17b)8/17c)11/17d)13/17Correct answer is option 'B'. Can you explain this answer?.
If tan θ + sec θ = 4, then find the value of cos θ ?a)5/17b)8/17c)11/17d)13/17Correct answer is option 'B'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about If tan θ + sec θ = 4, then find the value of cos θ ?a)5/17b)8/17c)11/17d)13/17Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If tan θ + sec θ = 4, then find the value of cos θ ?a)5/17b)8/17c)11/17d)13/17Correct answer is option 'B'. Can you explain this answer?.
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