How do you find cot 2B, given sin B = 12/13 and cos B < 0?

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How do you find cot 2B, given sin B = 12/13 and cos B < 0?

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Answer 1 · 2015-11-28T05:15:24

Find cot 2B, given $sin B = 12/13$ and cos B < 0

Ans: $119/120$

Explanation:

$sin B = 12/13$ .
Find cos B by the identity: $cos^2 a + sin^2 a = 1$
$cos^2 B = 1 - sin^2 B = 1 - 144/169 = 25/169$ --> $cos B = +- 5/13.$
$cos B = - 5/13$ (since cos B < 0)
Find: $sin 2B = 2sin B.cos B = 2(12/13)(-5/13) = - 120/169$
Find: $cos 2B = 2cos^2 B - 1 = 2(25/169) - 1 = - 119/169.$
Therefor: $cot 2B = cos (2B)/(sin 2B) = -119/169(169/-120) = 119/120$

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How do you find cot 2B, given sin B = 12/13 and cos B < 0?

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