Question

If − cot =4/5, then cosec A =​

Answer 1

Step-by-step explanation:

Cosec A - cot A = 4 / 5 (i) eqn.

Using identity :- cosec^2 - cot^2 A = 1

( a^2 - b^2 ) = ( a + b ) ( a - b )

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

(cosec A + cot A ) 4 / 5 = 1

cosec A + cot A = 5 / 4 (ii) eqn.

From (i) & (ii) eqn.

cosecA - cotA = 4 / 5

cosec A + cot A = 5/ 4

2 cosec A = 4/ 5 + 5 / 4

2 cosec A = 16 + 25 / 20

2 cosec A = 41 / 20

cosec A = 41 / 20 × 2

cosec A = 41 / 40

Hence option (D) is correct answer .