If 15 sec A = 17, find the other five trigonometric ratios of angle A.

1. 1 · Write what is given and what is to be found Given: sec A = 17/15 in right ΔABC with ∠B = 90°. To find: sin A, cos A, tan A, cosec A, cot A.
2. 2 · Draw the figure Right triangle ABC with the right angle at B. sec A = hypotenuse/adjacent, so AC = 17k and AB = 15k.
3. 3 · Write the formula or theorem Pythagoras theorem: AC² = AB² + BC². Reciprocal relation: cos A = 1/sec A.
4. 4 · Find the third side BC² = (17k)² − (15k)² = 289k² − 225k² = 64k², so BC = 8k.
5. 5 · Write the ratios
   • cos A = 15/17, sin A = 8/17, tan A = 8/15
   • cosec A = 17/8, cot A = 15/8
6. 6 · Check and box the answer Check: sin²A + cos²A = (64 + 225)/289 = 1. Box all five ratios.

Scoring tip: Always draw the triangle and write the sides as multiples of k. It shows the examiner your method even if one ratio slips.