Q. 315.0( 1 Vote )

# If 2 tan θ = 1, find the value of .

Given: 2 tan θ = 1

We know that,

Or

Let,

Side opposite to angle θ =AB = 1k

Side adjacent to angle θ =BC = 2k

where, k is any positive integer

Firstly we have to find the value of AC.

So, we can find the value of AC with the help of Pythagoras theorem

(AB)2 + (BC)2 = (AC)2

(k)2 + (2k)2 = (AC)2

(AC)2 = k2+4k2

(AC)2 = 5k2

AC =5k2

AC =±k5

But side AC can’t be negative. So, AC = k√5

Now, we will find the sin θ and cos θ

We know that

Side adjacent to angle θ = BC = 2k

and Hypotenuse = AC = k√5

So,

And

Side adjacent to angle θ =AB = 1k

And Hypotenuse =AC = k√5

So,

Now,

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