Question

Express the following in terms of trigonometric ratios of angles between 0° and 45°.

cos 51° + cot 49° – sec 47°

Answer 1

Given: cos 51° + cot 49° – sec 47°

Step-wise calculation:

1. Use complementary-angle identities: 

cos θ = sin(90° – θ)

cot θ = tan(90° – θ)

sec θ = cosec(90° – θ)

2. cos 51° = sin(90° – 51°) = sin 39°.

3. cot 49° = tan(90° – 49°) = tan 41°.

4. sec 47° = cosec(90° – 47°) = cosec 43°.

5. Substitute: cos 51° + cot 49° – sec 47° = sin 39° + tan 41° – cosec 43°.

cos 51° + cot 49° – sec 47° = sin 39° + tan 41° – cosec 43°, where 39°, 41° and 43° all lie between 0° and 45°.