Question

coseca-cota=2,find cosec^2a+cot^2a=?

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Answer 1

CoolestCat015

cosecA - cotA = 1/2 can be re - written as...

1/sinA - cosA/sinA=1/2

1 - cosA/sinA=1/2

2- 2cosA= sin A

cosA=2-sinA/2

use this

Answer 2

Answer:-

Given:-

Cosec a - cot a = 2 -- equation (1)

We know that,

cosec² a - cot² a = 1

Using (a² - b²) = (a + b) (a - b) we get,

→ (Cosec a + cot a) (Cosec a - cot a) = 1

Substituting Cosec a - cot a = 2 from equation (1) we get,

→ (Cosec a + cot a) (2) = 1

→ Cosec a + cot a = 1/2 -- equation (2)

Adding equations (1) & (2) we get,

→ Cosec a - cot a + Cosec a + cot a = 2 + 1/2

→ 2cosec a = (4 + 1)/2

→ Cosec a = 5/2 * 1/2

→ Cosec a = 5/4

Putting the value of Cosec a in equation (1) we get,

→ 5/4 - cot a = 2

→ 5/4 - 2 = cot a

→ (5 - 8) / 4 = cot a

→ cot a = (- 3/4)

Hence,

cosec² a + cot² a = (5/4)² + ( - 3/4)²

→ cosec² a + cot² a = 25/16 + 9/16

→ cosec² a + cot² a = (25 + 9)/16

→ cosec² a + cot² a = 34/16

→ cosec² a + cot² a = 17/8