If secθ – tanθ = 2, then find the value of cosθ
1. 3/5
2. 5/4
3. 2/5
4. 4/5
1. 3/5
2. 5/4
3. 2/5
4. 4/5
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Correct Answer – Option 4 : 4/5
Given:
Our equation is (secθ – tanθ) = 2
Formula used:
sec2θ – tan2θ = 1
Concept used:
(secθ – tanθ)(secθ + tanθ) = 1
If (secθ – tanθ) = p, then (secθ + tanθ) = 1/p
Calculation:
Our given expression is (secθ – tanθ) = 2 —-(1)
⇒ (secθ + tanθ) = ½ —-(2)
Adding equation (1) and (2)
⇒ 2secθ = 2 + 1/2
⇒ secθ = 5/4
∴ The value of cosθ is 4/5