Question

15. If cosecA - cot A =4/5 then find cosec A =​

Answer 1

Answer:

41/40

Step-by-step explanation:

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Answer 2

The value of $\csc A$ = $\dfrac{41}{40}$

Step-by-step explanation:

We have,

$\csc A$ - $\cot A$ = $\dfrac{4}{5}$                     ............ (1)

To find, the value of $\csc A$ = ?

We know that,

$\csc^2 A$ - $\cot^2 A$ = 1      

Using the algebraic identity,

$a^{2} -b^{2}$ = (a + b)(a - b)

⇒ ($\csc A$ + $\cot A$) (

Using equation (1), we get

⇒ ($\csc A$ + $\cot A$) ($\dfrac{4}{5}$ ) = 1

⇒ $\csc A$ + $\cot A$ = $\dfrac{5}{4}$          ............ (2)    

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

$\csc A$ - $\cot A$  +

⇒ 2$\csc A$ = $\dfrac{16+25}{20}$

⇒ $\csc A$ = $\dfrac{41}{2\times 20}$

⇒ $\csc A$ = $\dfrac{41}{40}$

∴ The value of $\csc A$ = $\dfrac{41}{40}$