Question

Why tanx × cotx = 1??????????

Answer 1

tanx = sinx ÷ cos x

:&

cotx = cosx ÷ sinx

tanx × cotx

sinx/cosx × cosx/sinx

1.

Answer 2

Solution :

Actually this question is based on the concept of Trigonometric identity. So , First of all , Let's revise Basic Trigonometry Identities.

Basic Trigonometry Identities :

↪ Sin²x + Cos²x = 1

↪ Sec²x - tan²x = 1

↪ tan x = 1/ cot x

↪ cotx = 1/tan x

Now, According to the Question !

Prove : tan x × cot x = 1

We can write tan x as 1/cot x , then

= tan x × cot x

= 1/cot x × cot x

$\sf{ \frac{1} { \cancel{cot \: x}} \times \: \cancel{cot \: x}}$

= 1 Proved !