Question:
If sec A + tan A = x, find the value of sin A in terms of x.
यदि sec A + tan A = x हो, तो sin A का मान x के रूप में क्या होगा?
Options:
- a) (x²-1)/(x²+1)
- b) (x+1)/(x-1)
- c) (x²+1)/(x²-1)
- d) 2x/(x²+1)
- a) (x²-1)/(x²+1)
- b) (x+1)/(x-1)
- c) (x²+1)/(x²-1)
- d) 2x/(x²+1)
correct answer : a)
Explanation:
sec A + tan A = x and sec A – tan A = 1/x. Adding: 2sec A = x+1/x, sec A = (x²+1)/(2x). Subtracting: 2tan A = x-1/x, tan A=(x²-1)/(2x). sin A = tan A/sec A = (x²-1)/(x²+1).
sec+tan=x, sec-tan=1/x। sin A = tan A/sec A = (x²-1)/(x²+1)।