Question

Without using trigonometric tables, evaluate:

`(tan 35^circ)/(cot 55^circ) + (cot 78^circ)/(tan 12^circ) = 2`

Answer 1

Given: `(tan 35^circ)/(cot 55^circ) + (cot 78^circ)/(tan 12^circ) = 2`

Step-wise calculation:

1. Use the co-function identity cot θ = tan (90° – θ).

2. cot 55° = tan (90° – 55°) = tan 35°

So, `(tan 35^circ)/(cot 55^circ) = (tan 35^circ)/(tan 35^circ)`

= 1

3. cot 78° = tan (90° – 78°) = tan 12° 

So, `(cot 78^circ)/(tan 12^circ) = (tan 12^circ)/(tan 12^circ)`

= 1

4. Sum: 1 + 1 = 2.

The expression equals 2.