If then find the values of sin A + cos A.

We know that,

Or

Given:

Let,

Side opposite to angle A =BC = k√3

Side adjacent to angle A =AB = 2k

where, k is any positive integer

Firstly we have to find the value of BC.

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

⇒ (AB)² + (BC)² = (AC)²

⇒ (2k)² + (√3k)² = (AC)²

⇒ (AC)² = 4 k² +3 k²

⇒ (AC)² = 7 k²

⇒ AC =√7 k²

⇒ AC =k√7

So, AC = k√7

Now, we will find the sin A and cos A

Side opposite to angle A = BC = k√3

and Hypotenuse = AC = k√7

So,

Now, we know that,

Side adjacent to angle A = AB =2k

Hypotenuse = AC = k√7

So,

Now, we have to find sin A +cos A

Putting values of sin A and cos A, we get