Answer:
Choice A is correct. tan∅ = - 4/3
Explanation:
We have given csc ∅ = 5/4 and 90 ⁰< ∅ < 180⁰.
We have to find tan ∅ = ?
csc ∅ = 5/4 is given.
As we know that :
cot²∅ = csc²∅ -1
cot²∅ = 25/16 - 1
cot²∅ = 9/16
Taking square root on both sides we get,
cot∅ = ± 3/4
As cot∅ is the reciprocal of tan∅ so,
tan∅ = ± 4/3
As we find the value of tan in the interval 90 ⁰< ∅ < 180⁰.
tan∅ is negative in this interval so, we take only negative value.
tan∅ = - 4/3 is the value of tan∅.