Question

if tan 2A = (A-18), where 2A is an acute angle, find the value of A

Answer 1

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A = 36°

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As we know that,

$\tt\longrightarrow cot(90 - x) = tan \: x \\ \\ \tt °.° \: \: \: \green{ tan \: 2A = cot ( A - 18)} \\ \\ \tt \longrightarrow cot(90 - 2A) = cot(A - 18) \\ \\ \tt \longrightarrow \cancel{cot}(90 - 2A) = \cancel{cot}(A - 18) \\ \\ \tt \longrightarrow90 - 2A = A - 18 \\ \\ \tt \longrightarrow - 2A - A = - 18- 90 \\ \\ \tt \longrightarrow -3A = - 108 \\ \\ \tt \longrightarrow \cancel - 3A = \cancel - 108 \\ \\ \tt \longrightarrow A = \frac{ \cancel{108}}{ \cancel3} \\ \\ \tt \longrightarrow \red{ A = 36°}$

Therefore, the value of A is 36°.

Answer 2

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Given tan2A=cot(A−180)

⇒cot(90−2A)=cot(A−180)[∵tanθ=cot(90−θ)]

Comparing angles we get

90−2A=A−18

⇒90+18=A+2A

⇒3A=108

⇒A=108/3

⇒A=36∘