EXAMPLES
Ex 1:
The value of tan 225° + cot 135°
Sol:
| Sol: tan 225° + cot 135° | = | tan (180° + 45°) + cot (180° - 45°) |
| = | tan 45° – cot 45° | |
| = | 1 – 1 | |
| = | 0 |
Ex 2:
Sol:
Ex 3:
If sec 5A = cosec(A – 36°), where 5A is an acute angle, find the value of A.
Sol:
| sec 5A | = | cosec(A – 36°) |
| cosec(90° – 5A) | = | cosec(A – 36°) |
| (90° – 5A) | = | (A – 36°) |
| –5A – A | = | –36° – 90° |
| –6A | = | –126° |
| ∴ A | = | 21° |
Ex 4:
Evaluate tan 9°, tan 27°, tan 63°, tan 81°.
Sol:
| tan 9° tan 27° tan 63° tan 81° | = | (tan 9° tan 81°)(tan 27° tan 63°) |
| = | (tan 9° tan(90° - 9°)) (tan 27° tan (90° - 27°)) | |
| = | (tan 9° cot 9°)(tan 27° cot 27°) | |
| = |  |
|
| = | 1 × 1 | |
| = | 1 |
Ex 5:
If A, B and C are interior angles of a triangle ABC, then show that 
Sol:
We know that, A + B + C = 180°
A + B = 180° – C
Ex 6:
Express cot 60° + cos 70° in terms of trigonometric ratios of angles between 0° and 45°.
Sol:
| cot 60° + cos 70° | = | cot(90° – 30°) + cos(90° – 20°) |
| = | tan 30° + sin 20° |