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What is the value of the following?

tan 31° tan 33° tan 35° _ _ _ _ _ tan 57° tan 59°


1. -1
2. 0
3. 1
4. 2

1 Answer

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Correct Answer - Option 3 : 1

Concept:

tan A = cot (90- A)

cot A = \(\rm \frac{1}{tan A}\)

Calculation:

Given,

tan 31° tan 33° tan 35° _ _ _ _ _ tan 57° tan 59°

⇒ tan 31° tan 33° tan 35° _ _ _ _ _ cot (90° -  57°)  cot (90° - 59°)

 tan 31° tan 33° tan 35º _ _ _ _ _  cot 33° cot 31°

 tan 31° tan 33° tan 35º _ _ _ _ _  \(\rm \frac{1}{tan 33^{\circ}}\) \(\rm \frac{1}{tan 31^{\circ}}\)

tan 45° × 1 = 1

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