Question

cosecA+cotA=2, then cosecA=? ​

Answer 1

Answer:

⇒ cosec A = $\frac{5}{4}$

Step-by-step explanation:

Given :

cosec A + cot A = 2

Find cosec A

Solution :

cosec A + cot A = 2 ..(i)

We know that,

cosec² A - cot² A = 1

a² - b² = (a + b)(a - b)

⇒ (cosec A + cot A)(cosec A - cot A) = 1

⇒ cosec A - cot A = $\frac{1}{cosecA+cotA} = \frac{1}{2}$

⇒ cosec A - cot A = $\frac{1}{2}$ ...(ii)

By adding (i) & (ii)

⇒ (cosec A + cot A) + (cosec A - cot A) = $2 + \frac{1}{2}$

⇒ 2 cosec A = $\frac{4 + 1}{2} = \frac{5}{2}$

⇒ cosec A = $\frac{5}{4}$