SOLUTION: If tan(theta) is given then how to find out the value of sin(theta)+cos(theta)

There are two methods, right triangle and identities.

Either method you use, you will have to go by what quadrants are 
possible for theta.  If the tangent is a positive number, theta
is either in QI or QIII.  If the tangent is negative, theta is in
QII or QIV.

One way is to make a triangle like this in whatever quadrant
theta is in.  I have the triangle drawn below in the first
quadrant, but you can draw it in whichever quadrant theta is in.

 

Since you know the tangent, you can use the Pythagorean theorem
to find the hypotenuse.  Then the sine is opposite/hypotenuse,
and the cosine is adjacent/hypotenuse.

Then add the sine and the cosine.
  
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Another way is to use identities:

Use  to find  and .

Then use  to find .

Then use  to find .

Then add the sine and the cosine.

Edwin