If sin x = 5/13 and x lies in (0°, 90°), then find the value of: [(1 + cos x) / (1 - cos x)]
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Correct answer: A
Explanation
given :
sin x = 5/13
x ∈ (0°, 90°)
According to the formula:
sin²x + cos²x = 1
sin x = 5/13
cos x = √(1 − sin²x)
cos x = √(1 − 25/169)
cos x = √(144/169)
cos x = 12/13
(1 + cos x) / (1 − cos x)
= (1 + 12/13) / (1 − 12/13)
= (25/13) / (1/13)
= 25