If 3 tan A = 4, then the value of the given expression is:
A
1/7
B
√2/7
C
1/√7
D
√3/√7
Correct Option:
C
Explanation
From 3 tan A = 4, tan A = 4/3. Using a 3–4–5 triangle, sin A = 4/5 and cos A = 3/5, so sec A = 5/3 and cosec A = 5/4. Therefore, (sec A − cosec A)/(sec A + cosec A) = (5/3 − 5/4)/(5/3 + 5/4) = 1/7, and the square root of this value is 1/√7.
