If will be the value of sec279° - (1/tan211°)?

1.	If will be the value of sec279° - (1/tan211°)?
Answer» 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

Answer» 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

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