Question

Find the value of A if $\tan 2A=\cot (A-{24}^0)$.

Answer 1

Hint: Use the information, $\tan 2A=\cot (A-{24}^0)$ and solve carefully.

Complete step-by-step answer:
Consider the given equation, $\tan 2A=\cot (A-{24}^0)$. We know that, $\tan \theta =\cot ({90}^{\circ }-\theta )$.

Using this formula in the given equation,
$$\begin{gathered} \tan 2A=\cot (A-{24}^0) \\ \Rightarrow \cot ({90}^{\circ }-2A)=\cot (A-{24}^0) \\ \Rightarrow {90}^{\circ }-2A=A-{24}^0 \\ \Rightarrow 3A={114}^{\circ } \\ \Rightarrow A={38}^{\circ } \end{gathered}$$

Note: It’s always better to learn and understand the formulas. Especially in trigonometry. In trigonometry, if we talk about problem solving then formulas play a vital role in that.