If will be the value of sec279° – (1/tan211°)?
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Correct Answer – Option 2 : 1
Given:
The given expression is sec279° – (1/tan211°)
Formula Used:
Basic concept of trigonometric ratio and identities
We know that
Sec2 θ – tan2 θ = 1
1/tan θ = cot θ
Cot (90 – θ) = tan θ
Calculation:
The given expression sec279° – (1/tan211°) can be written as sec279° – cot211°
∵ 1/tan θ = cot θ
Now, sec279° – cot211° = sec279° – cot2(90 – 79°) = sec279° – tan2 79°
∵ sec2θ – tan2θ = 1
∴ sec279° – tan279° = 1
Hence, option (2) is correct