Krishna
0

Step 1: Explore the given question.

            NOTE: \tan A = \sqrt{3}  

                         We can write this as \tan A =\frac{\sqrt{3}}{1}

                          Compare with: \tan A = \frac{opposite}{adjacent}

                Therefore, In a right angle triangle  opposite side = \sqrt{3}

                                                                         adjacent side = 1

    

Step 2: Construct a right triangle with known measurements and find the unknown length of the side.

                  

                  hypotenuse^2 = opposite^2 + adjacent^2

                hyp^2=\left(\sqrt{3}\right)^2+1^2

                hyp=\sqrt{4}

                      hypotenuse = 2


Step 3: Find the values of the trigonometric ratios

             EXAMPLE: \sin A = \frac{opp}{hyp} = \frac{\sqrt{3}}{2}

                                 \sin C = \frac{opp}{hyp} = \frac{1}{2}

                               \cos A = \frac{adj}{hyp} = \frac{1}{2}

                               \cos C = \frac{adj}{hyp} = \frac{\sqrt{3}}{2}


Step 4: Substitute the calculated values in the given equation and simplify

              =   \sin A \cos C + \cos A \sin C

               = \frac{\sqrt{3}}{2}*\frac{\sqrt{3}}{2} + \frac{1}{2} * \frac{1}{2}

                =   \frac{3}{4}+ \frac{1}{2}

                 = 1