Question

If cosA=12/13then find cosecA and cotA

Answer 1

cos A = 12k/13k = b/h
p = √h^2 - b^2
p = √(13k)^2 - (12)^2
p = √169k^2 - 144k^2
p = √25k^2
p = 5k

cosec A = h/p = 13k/5k = 13/5
cot A = b/p = 12k/5k = 12/5

Answer 2

cos A = 12/13
now sin²A + cos²A = 1
therefore sin²A + 12 * 12 / 13² = 1
sin²A = 1 - 144/169
sin²A = 169 - 144/169
sin²A = 25/169
sinA = 5/13
cosecA = 1/sinA = 13/5
cotA = cosA/sinA = 12/13 * 13/5 = 12/5
therefore cosecA = 13/5 and cotA = 12/5
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