Question

Evaluate tan35 tan40 tan45 tan50 tan55

Answer 1

= tan35° × tan40° × tan45° × tan50° × tan55°
= tan35° × tan40° × tan45° × tan(90°—40°) × tan(90°—35°)
=tan35° × tan40° × tan45° × cot40° × cot35°
=tan35° × tan40° × tan45° × (1÷tan40°) × (1÷tan35°)
=tan45°
=1

Answer 2

1

Step-by-step explanation:

Given,

Tan35° * Tan40° * Tan45° * Tan50° * Tan55°

⇒ (Tan 90° - 55°) * (Tan90° - 50°) * 1 * Tan50° * Tan55°

= Cot55° * Cot50° * Tan50° * Tan55°

= 1/Tan55° * 1/Tan50° * Tan50° * Tan55°

= 1

∵ 1 is the value we get after evaluating tan35 tan40 tan45 tan50 tan55.

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