Question

Evaluate without using trigonometric tables :

tan 20 .tan 40 .tan 50 .tan 70.​

Answer 1

Answer:

Answer: cotx=tan(90-x). and cotx=1/tanx. so tan20×tan70=tan20×cot20=1. similarly tan50=cot40. hence tan40×tan50=1.

Answer 2

Required Answer:-

We have to evaluate:

$\rm{ \tan(20) . \tan(40) . \tan(50) . \tan(70) }$

By the concept of complementary angles:

sin x = cos (90-x)

tan x = cot (90-x)

sec x = cosec(90-x) and vice versa..

Then,

Assuming they are in degrees (°)

➻ tan 20. tan 40. tan (90 - 40). tan (90 - 20)

➻ tan 20. tan 40. cot 40. cot 20

➻ tan 20. cot 20. tan 40. cot 40

➻ 1 × 1 = 1 (A)

(Because we know that, tan x. cot x = 1)

Note:

Complementary angles are the angles that add upto 90°. Like in the above case,

20° and 70° are complementary angles.

40° and 50° are complementary angles.