Question

given :tanA =4/3, find:cosecA/cotA-secA

Answer 1

Answer:

Step-by-step explanation:

Answer 2

tanA =4/3
1+tan square A= sec square A
1+(4/3) square A=sec square A
1+16/9A = sec square A
(9+16)/9 A= sec square A
25/9 A= sec square A
Taking square root on both sides
sec A=5/3

tanA= 1/cot A
4/3=1/cot A
cot A=3/4

1+cot square A= cosec square A
1+(3/4) square A= cosec square A
1+ 9/16 A =cosec square A
(16+9)/16 A = cosec square A
25/16 A= cosec square A
Taking square root on both sides
cosec A= 5/4

cosec A= 5/4
cot A=3/4
sec A=5/3

cosec A / cot A - sec A
=(5/4)/(3/4) - (5/3)
=5/3×4/3 - 5/3
=20/9 -5/3
=20/9 - 5/3×3/3
=20/9 - 15/9
=(20-15)/9
=5/9
Answer: 5/9