Question

without using trigonometric tables prove that tan 1 degree tan 11 degree tan 21 degree tan 69 degree tan 79 degree tan 89 degree=1

Answer 1

Tan(90°-89°)×tan(90°-79°)×tan(90°-69°)×tan69°×tan79°×tan89°
Cot89°×cot79°×cot69°×tan69°×tan79°×tan89°
=1. (Tan theta ×cot theta =1)

Answer 2

Tan(90°-89°)×tan(90°-79°)×tan(90°-69°)×tan69°×tan79°×tan89°
Cot89°×cot79°×cot69°×tan69°×tan79°×tan89°
=1. (Tan theta ×cot theta =1)