Question

if 5sin A = 3 find sec A - cosec A

Answer 1

Answer:

we have ......

5 sin A = 3

then .. sin A = 3/5

WKT.......

sin *2 (A). + cos *2 (A ) = 1

( 3/5 ) *2 + cos*2 (A) = 1

cos*2 (A) = 1 - 9/25

cos*2 (A) = 25 - 9 /25

cos*2 ( A) = 16/15

cos (A) = 4/5

then .... we find ..

sec A = 5/4

cosec A = 5/3

then.....

sec A - cosec A

5/4 - 5/3

15/12 - 20/12

-5/12 ....

hence sec A - cosec A = -5/12 .....

..... Hope you are understand .......

Answer 2

Answer:

secA - cosecA = -5/12

Step-by-step explanation:

Given that, sinA = 3/5

WKT,

cos²A= 1 - sin²A

=1 - (3/5)²

= 1 - 9/25

=(25 - 9)/25

=16/25

cos²A = 16/25

cosA = 4/5

secA - cosecA = 1/cosA - 1/sinA

=1/4/5 - 1/3/5

= 5/4 - 5/3

=(15 - 20)/12

= -5/12