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}

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

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