Question

find the value of cosec (120) , sec(120) and cot(120)?

Answer 1

Answer:

a) cosec120 = $\frac{2}{\sqrt{3}}$

b)sec120° =-√2

c)cot120°=$\frac{-1}{\sqrt{3}}$

Explanation:

___________________________

By Trigonometric Ratios of Complementary angles :

i) cosec(90+A) = secA

ii) sec(90+A) = -cosecA

iii) cot(90+A) = -tanA

__________________________

Now,

a) cosec120

= cosec(90+30)

= sec30°

= $\frac{2}{\sqrt{3}}$

b) sec120°

= sec(90°+30°)

= -cosec30°

= -√2

c) cot120°

= cot(90°+30°)

= -tan30°

= $\frac{-1}{\sqrt{3}}$

••••

Answer 2

Answer

cosec(90+A) = secA

sec(90+A) = -cosecA

cot(90+A) = -tanA

So, here

cosec120

cosec(90+30)

sec30°

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

32

sec120°

sec(90°+30°)

-cosec30°

= -√2

cot120°

cot(90°+30°)

-tan30°

$\frac{-1}{\sqrt{3}}3-1$