Question

Trigonometry

Answer 1

Answer:

3 + 2sqrt(3)/3

Step-by-step 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

Answer:

$\frac{9 + 2 \sqrt{3} }{3}$

Step-by-step explanation:

$\cosec(30) + \cosec(60) + \cosec(90) \\ \\ = 2 + \frac{2}{ \sqrt{3} } + 1 \\ \\ = \frac{2 \sqrt{3 } + 2}{ \sqrt{3} } + 1 \\ \\ = \frac{2 \sqrt{3} + 2 + \sqrt{3} }{ \sqrt{3} } \\ \\ = \frac{3 \sqrt{3} + 2}{ \sqrt{3} } \\ \\ = \frac{3 \sqrt{3} + 2}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } \\ \\ = \frac{9 + 2 \sqrt{3} }{3}$