If secθ - tanθ = 3, then cosθ is equal to:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e 3/5.
| Understanding/Application |
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secθ – tanθ = 3 ....(1 (secθ – tanθ) × (secθ + tanθ)/(secθ + tanθ) = 3 (sec2θ – tan2θ)/(secθ + tanθ) = 3 1/(secθ – tanθ) = 3 secθ + tanθ = 1/3 ....(2 |
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Adding 1 and 2 we get - 2secθ = (3 + 1/3) 2secθ = 10/3 secθ = 5/3 cosθ = 3/5 |