△ABC is right angled at B. If secA=
3
5
, then what is the value of cosec C?
- A5/3
- B3/4
- C4/5
- D4/3
Solution & Step-by-step Explanation
In a right-angled triangle △ABC, right-angled at B:
∠A+∠C=90
∘
⟹C=90
∘
−A
We need to find the value of cosec C:
cosec C=cosec(90
∘
−A)
Using the trigonometric co-function identity cosec(90
∘
−θ)=secθ:
cosec(90
∘
−A)=secA
Given that secA=
3
5
:
cosec C=
3
5
∠A+∠C=90
∘
⟹C=90
∘
−A
We need to find the value of cosec C:
cosec C=cosec(90
∘
−A)
Using the trigonometric co-function identity cosec(90
∘
−θ)=secθ:
cosec(90
∘
−A)=secA
Given that secA=
3
5
:
cosec C=
3
5