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If tan2A\ =\ cot(A-18^@), where 2A is an...

If `tan2A\ =\ cot(A-18^@),` where 2A is an acute angle, find the value of A.

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To solve the equation \( \tan 2A = \cot (A - 18^\circ) \), we can follow these steps: ### Step 1: Rewrite the equation using trigonometric identities. We know that \( \cot \theta = \tan (90^\circ - \theta) \). Therefore, we can rewrite the right-hand side: \[ \tan 2A = \cot (A - 18^\circ) = \tan (90^\circ - (A - 18^\circ)) = \tan (90^\circ - A + 18^\circ) = \tan (108^\circ - A) \] ...
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Knowledge Check

  • If sec 2A=cosec (A-42^@) , where 2A is an acute angle, find the value of A.

    A
    `A=44^@`
    B
    `A=54^@`
    C
    `A=64^@`
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    C
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    D
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