Question:
Prove that cos^-1 5/13 = tan^-1 (12/5)
Answer:
We know that cos-1 x = tan-1 {√(1 - x2 )/x }
So, cos-1 (5/13) = tan-1 [√{(1 - (5/13)2 }/(5/13)]
=> cos-1 (5/13) = tan-1 [√{(1 - (25/169)}/(5/13)]
=> cos-1 (5/13) = tan-1 [√{(169 - 25/169)}/(5/13)]
=> cos-1 (5/13) = tan-1 [√(144/169)/(5/13)]
=> cos-1 (5/13) = tan-1 [(12/13)/(5/13)]
=> cos-1 (5/13) = tan-1 (12/5)
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