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mojhsa [17]
3 years ago
14

Trigonometry

Mathematics
2 answers:
never [62]3 years ago
8 0

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

quester [9]3 years ago
4 0

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}

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