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Trigonometric identities sheet
3-mark answer frame

Prove that sin²A + cos²A = 1 for an acute angle A. Hence prove that 1 + tan²A = sec²A.

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · Write what is given and what is to be found Given: ΔABC with ∠B = 90°. To prove: sin²A + cos²A = 1 and 1 + tan²A = sec²A.
  2. 2 · Draw the figure Right triangle ABC with the right angle at B. Mark ∠A. Label AB adjacent, BC opposite, AC hypotenuse.
  3. 3 · Write the formula or theorem By Pythagoras theorem, AB² + BC² = AC².
  4. 4 · Divide by AC² (AB/AC)² + (BC/AC)² = 1, so cos²A + sin²A = 1.
  5. 5 · Divide by cos²A sin²A/cos²A + cos²A/cos²A = 1/cos²A, so tan²A + 1 = sec²A.
  6. 6 · Check and box the answer State the range: the first holds for 0° ≤ A ≤ 90°, the second for 0° ≤ A < 90°. Write 'Hence proved'.

Scoring tip: Name the theorem (Pythagoras) in words and show the division by AC² on its own line. That line carries the method mark.