If in a right-angled triangle, cos A = 5/13, find the value of tan A - sin A.
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Correct answer: D
Explanation
given :
cos A = 5/13
According to the formula:
sin²A + cos²A = 1
cos A = 5/13
sin A = √(1 − cos²A)
sin A = √(1 − 25/169)
sin A = √(144/169)
sin A = 12/13
tan A = sin A / cos A
tan A = (12/13) ÷ (5/13)
tan A = 12/5
tan A − sin A
= 12/5 − 12/13
= (156 − 60) / 65 = 96/65