Question

without using trigonometric tables prove that :tan 1° tan 11° tan 21° tan 69° tan 79° tan 89°

Answer 1

tan1° × tan11° ×tan21°× tan69°× tan79° × tan89°

tan1°×tan89°×tan11°×tan79°×tan21°×tan69°

tan1°tan(90-1)×tan11°tan(90-11)×tan21°tan(90-21)

tan1° cot1° × tan11° cot11° × tan21°cot21

[tan1° * 1/tan1°] × [tan11° *1/tan11°] × [tan21° * 1/cot21°]


1 × 1 ×1 

1


i hope this will help you

-by ABHAY

Answer 2

Hii friend,

Tan 1° × Tan 11° × Tan 21° × Tan 69° × Tan 79° × Tan 89°.

Tan 1° × Tan 89° × Tan 11° × Tan 79° × Tan 21° × Tan 69.

Tan (90° - 89° ) × Tan 89° × Tan (90° - 79° ) × Tan 79° × Tan (90°-69°) × Tan 69°

Cot 89° × Tan 89° × Cot 79° × Tan 79° × Cot 69° × Tan 69°. [ Tan (90- theta ) = Cot theta]

Cot 89° × 1/Cot 89° × Cot 79° × 1/ Cot 79° × Cot 69° × 1/ Cot 69°. [ Tan theta = 1/Cot theta].

1 × 1 × 1 = 1 Ans.


HOPE IT WILL HELP YOU.... :-)