Is cot 4 a is equal to tan (a - 20) where 4a is an acute angle find the value of a

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asked Nov 8, 2023 16.2k views

14 votes

Is cot 4 a is equal to tan (a - 20) where 4a is an acute angle find the value of a

Mathematics
college

Wouter Overmeire asked

by Wouter Overmeire

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1 Answer

12 votes

Answer:

a = 22

Explanation:

$cot \: 4a = tan \: (a - 20)....(given) \\ \\ \implies \: tan(90 - 4a) = tan \: (a - 20) \\ [\because \: cot \theta = tan(90 \degree - \theta) ]\\ \\ \implies (90 - 4a) = tan(a - 20) \\ \\ \implies \: 90 + 20 = 4a + a \\ \\\implies \: 110 = 5a \\ \\ \implies \: a = (110)/(5) \\ \\ \huge \red{ \boxed{\implies \: a = 22}}$

Ryan Cavanaugh answered Nov 14, 2023