Trigonometry — Practice

Question 1

Evaluate: sin²30° + cos²60° − 2 sin 45° cos 45°

Accepted Answer

sin 30° = 1/2 → sin²30° = 1/4. cos 60° = 1/2 → cos²60° = 1/4. sin 45° = cos 45° = 1/√2. sin 45° × cos 45° = 1/√2 × 1/√2 = 1/2. Expression = 1/4 + 1/4 − 2(1/2) = 1/2 − 1 = −1/2.

Question 2

Prove: (1 − sin A)/(1 + sin A) = (sec A − tan A)²

Accepted Answer

RHS = (sec A − tan A)² = (1/cos A − sin A/cos A)² = ((1 − sin A)/cos A)² = (1 − sin A)²/cos²A = (1 − sin A)²/(1 − sin²A) = (1 − sin A)²/[(1 − sin A)(1 + sin A)] = (1 − sin A)/(1 + sin A) = LHS ✓.

Practice — Trigonometry

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