Question

Without using trigonometric tables, evaluate:

`(tan 65^circ)/(cot 25^circ)`

Answer 1

Given: `(tan 65^circ)/(cot 25^circ)`

65° = 90° – 25°

So, tan 65° = tan (90° – 25°). 

Use the complementary-angle identity tan (90° – θ) = cot θ.

Therefore, tan 65° = cot 25°.

So, `(tan 65^circ)/(cot 25^circ) = (cot 25^circ)/(cot 25^circ)`

= 1