Question

Evaluate : $\frac{\tan 65°}{\cot 25°}$

Answer 1

Applying the trigonometric identities:

We know that,

$\tan \left(90°-\mathrm{A}\right)=\mathrm{cotA}$

So, from above,

$$\begin{gathered} \frac{\tan 65°}{\cot 25°} \\ =\frac{\tan (90°-25°)}{cot25°} \\ =\frac{cot25°}{cot25°} \\ =1 \end{gathered}$$

Hence, the value of $\frac{\tan 65°}{\cot 25°}=1$.