Question

tan x + cot x = 2 , cos x = ?​

Answer 1

Answer:

In this question Tan and cot have to have same value

Step-by-step explanation:

So the value in which tan and cot will be equal is 45 that is pi/4

Which is equal to 1

So tan 45+ cot 45 is equal to 2

So cot 45 is 1

Answer 2

Answer:

1 / √2.

Step-by-step explanation:

From the properties of trigonometry :

 tanA = sinA / cosA

 cotA = cosA / sinA  

 sin^2 A + cos^2 A = 1

Here,

⇒ tan x + cot x = 2

⇒ ( sinx / cosx ) + ( cosx / sinx ) = 2

⇒ ( sin^2 x + cos^2 x ) / sinx.cosx = 2

⇒ 1 / sinx.cosx = 2

⇒ 1 = 2.sinx.cosx

   Square on both sides :

⇒ 1^2 = ( 2sinx.cosx )^2

⇒ 1 = 4.sin^2 x . cos^2 x

⇒ ( 1 / 4 ) = ( 1 - cos^2 x )cos^2 x

⇒ 1 / 4 = cos^2 x - cos^4 x

         let cos^2 x = a

⇒ 1 / 4 = a - a^2

⇒ 1 = 4a - 4a^2

⇒ 4a^2 - 4a + 1 = 0

⇒ ( 2a - 1 )^2 = 0

⇒ a = 1 /2    ⇒ cos^2 x = 1 / 2

⇒ cosx = 1 /√2

        Hence the required value of cosx is 1 / √2