1.

If tan(x + y) × tan(x – y) = 1, then find the value of tanx.

Answer» Correct Answer - Option 3 : 1

Given:

tan(x + y) × tan(x – y) = 1

Concept used:

If tanA × tanB = 1, then A + B = 90°

Calculation:

tan(x + y) × tan(x – y) = 1

⇒ x + y + x – y = 90°

⇒ 2x = 90°

⇒ x = 45°

⇒ tan45° = 1

∴ tan45° is 1.


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