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

1 Answer
Nghi N.
Nov 28, 2015

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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