Question

If tan 2A = cot(A-18°),where 2A is an acute angle .Find the value of A

Answer 1

Given that

tan 2A = cot(A-18°)

⇒ tan 2A = tan[π/2-(A-18°)]             [ since tan(π/2-Ф)=cotФ ]

⇒ 2A = π/2-(A-18°)

⇒ 2A = π/2-A+18°

⇒ 3A = 90°+18°

⇒ 3A = 108°

⇒ A = 108°/3

⇒ A = 36°

Answer 2

Answer: answer is 36°

Step-by-step explanation:given, tan 2A= cot(A-18°)

tan 2A = cot(A-18°)

but, tan 2A can be also written as cot (90° - 2A){TRIGONOMETRIC RATIOS}

∴, cot(90°-2A) = cot(A-18°)

∴ 90°-2A = A-18°

∴          3A = 108°

              A = 108\3

                  = 36°

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