1.

Find the value: 1 + tan15°tan75° 1. sec215° 2. sec275° 3. 24. \(1 + {{1 + \sqrt 3} \over 2}\)

Answer» Correct Answer - Option 3 : 2

Formula used:

tanθ = cot(90° – θ)

cotθ = 1/tanθ 

Calculation:

tan75° = cot(90° – 75°)

⇒ tan75° = cot15° 

cot15° = 1/tan15° 

We have to find the value of 1 + tan15°tan75° 

⇒ 1 + tan15° × cot15° 

⇒ 1 + tan15°/tan15° 

⇒ 1 + 1 = 2

∴ The value of the given expresison is 2



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