Question

Trigonometry

Special Right Triangles
Find the exact value of cosec 30* + cosec 60* + cosec 90*.

Answer 1

3 + 2sqrt(3)/3

Explanation:

sin(30) = ½

cosec(30) = 2

sin(60) = sqrt(3)/2

cosec(60) = 2/sqrt(3) or 2sqrt(3)/3

sin(90) = 1

cosec(90) = 1

2 + 2sqrt(3)/3 + 1

3 + 2sqrt(3)/3

Answer 2

`(9 + 2 √(3) )/(3) \\`

Explanation:

`\cosec(30) + \cosec(60) + \cosec(90) \\ \\ = 2 + (2)/( √(3) ) + 1 \\ \\ = (2 √(3 ) + 2)/( √(3) ) + 1 \\ \\ = (2 √(3) + 2 + √(3) )/( √(3) ) \\ \\ = (3 √(3) + 2)/( √(3) ) \\ \\ = (3 √(3) + 2)/( √(3) ) * ( √(3) )/( √(3) ) \\ \\ = (9 + 2 √(3) )/(3)`