If cos x = 12/13 and x ∈ (0°, 90°), then find the value of [(1 + sin x)² + (1 - sin x)²] / cos²x.
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Correct answer: C
Explanation
Has been given :
cos x = 12/13, x ∈ (0°, 90°)
According to the formula:
sin²x + cos²x = 1
sin x = √(1 − cos²x)
= √(1 − 144/169)
= √(25/169)
= 5/13
(1 + sin x)² + (1 − sin x)²
= 1 + 2sinx + sin²x + 1 − 2sinx + sin²x
= 2 + 2sin²x
= 2 + 2(25/169)
= 2(1 + 25/169)
= 2(194/169)
= 388/169
cos²x = (12/13)²= 144/169
[(1 + sin x)² + (1 − sin x)²] / cos²x
= (388/169) / (144/169)
= 388/144
= 97/36