If tan θ + sec θ = 4, then the value of cos θ is equal to :यदि tan θ + sec θ = 4, तो cos θ का मान बराबर है :

1. A17/8
2. B8/17
3. C15/17
4. D17/15

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Correct answer: B. 8/17

Explanation

Since sec²θ − tan²θ = 1, we get (sec θ + tan θ)(sec θ − tan θ) = 1, so sec θ − tan θ = 1/4. Adding this to sec θ + tan θ = 4 gives 2 sec θ = 17/4, i.e. sec θ = 17/8. Therefore cos θ = 8/17.चूँकि sec²θ − tan²θ = 1, अतः (sec θ + tan θ)(sec θ − tan θ) = 1 से sec θ − tan θ = 1/4 प्राप्त होता है। इसे sec θ + tan θ = 4 में जोड़ने पर 2 sec θ = 17/4, अर्थात् sec θ = 17/8। अतः cos θ = 8/17।