Question

find the value of, 2 cot2 A +2 if sin A = 1/3​

Answer 1

Step-by-step explanation:

sinA = 1/3

opp/hyp = 1/3

by pythagoras theorem

(opp)^2 + (adj)^2 = (hyp)^2

(1)^2 + (adj)^2 = (3)^2 => (adj)^2 = 9 - 1 => 8

$so \: adjacent \: side \: = \sqrt{8} \\ so \: cos(a) = \sqrt{8} /3 \: = adj/hyp\\ we \: know \: that \: \cot(a) = cos(a) \div sin(a) \\ \cot(a) = \sqrt{8} /3 \: \div \: 1 /3 \\ \cot(a) = \sqrt{8} \\ {cot}^{2} a = (\sqrt{8}) ^{2} \\ 2 {cot}^{2} a + 2 = 2 \times 8 + 2 \\ = 18$

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