Question

If tan 2 A = cot (A − 12°), where 2 A is an acute angle, find the value of A.

Answer 1

\[\begin{array}{l}sin3A = \cos(A - {26}^\circ ) \\ \end{array}\]
\[\begin{array}{l}\Rightarrow cos( {90}^\circ - 3A) = \cos(A - {26}^\circ )[ \because \sin\theta = \cos( {90}^\circ- \theta)] \\ \end{array}\]
\[\begin{array}{l}\Rightarrow {90}^\circ- 3A = A - {26}^\circ \\ \end{array}\]
\[\begin{array}{l}\Rightarrow {116}^\circ = 4A \\ \end{array}\]
\[ \Rightarrow A = \frac{{116}^\circ}{4} = {29}^\circ \]