Suppose that tan theta 12 and 0 degree Solutiontan theta12

Suppose that tan theta = 1/2 and 0 degree

Solution

tan theta=1/2

so here oppsite=1 and adjacent=2

Therefore hypotenuse = sqrt 5

Hence cos theta= 2/sqrt5

cos theta/2= sqrt(1+costheta)/2

                  = sqrt (1 + 2/sqrt5)/2

                 = sqrt(sqrt5 + 2)/2sqrt 5

Multiplying both top and bottom by sqrt 5 inside the square root we get

       = sqrt((5 + 2sqrt5)/10)

tan theta/2= (1-cos theta)/sin theta

And sin theta= 1/sqrt 5

Therefore tan theta/2= (1-2/sqrt5)/1/sqrt 5

                                  = sqrt 5 -2