Question

Evaluate the following:

`(cot 40^circ)/(tan 50^circ) - 1/2(cos 35^circ/sin 55^circ)`

Answer 1

Given: `(cot 40°)/(tan 50°) - 1/2 (cos 35^circ/sin 55^circ)`

Step-wise calculation:

1. Use complementary-angle identities: cot θ = tan(90° – θ) and sin(90° – θ) = cos θ.

Hence cot 40° = tan 50° and sin 55° = cos 35°.

2. Substitute: `(cot 40^circ)/(tan 50^circ) = (tan 50^circ)/(tan 50^circ) = 1`.

3. And `(cos 35^circ)/(sin 55^circ) = (cos 35^circ)/(cos 35^circ) = 1`

So `(1/2)(cos 35^circ/sin 55^circ) = 1/2`.

4. Therefore the whole expression = `1 - 1/2 = 1/2`.