Question

Find the exact value of tan30⁰ × cos30⁰
give your answer in its simplest form​

Answer 1

tan(30⁰)=√3/3

cos(30⁰)=√3/2

switch sides:

sin(x) /√3/2 =√3/3

multiply both sides by 3:

3·sin(x) /√3/2 =3·√3/3

simplify:

2√3 sin (x) =√3

divide both sides by 2√3:

2√3 sin (x) / 2√3 = √3 / 2√3

simplify:

sin (x)= 1/2