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If 0 < x < (π/4), then what is the value if √2 - 2 tanx cotx
1. 1
2. √2 - 2
3. 0
4. 1/2

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Correct Answer - Option 2 : √2 - 2

Given

√2 - 2 tan x cot x

Formula used

tan 30° = (1/√3)

cot 30° = √3

Calculation

√2 - 2 tan30° cot30°

⇒ √2 - 2 × (1/√3) × (√3)

⇒ √2 - 2

∴ The value of √2 - 2 tan x cot x is √2 - 2.

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