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प्रश्न
Express the following in terms of trigonometric ratios of angles between 0° and 45°.
sin 67° + cos 75°
योग
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उत्तर
Given: sin 67° + cos 75°
Step-wise calculation:
1. Use co-function identities: sin θ = cos(90° – θ) and cos θ = sin(90° – θ).
2. sin 67° = cos(90° – 67°) = cos 23°.
3. cos 75° = sin(90° – 75°) = sin 15°.
4. Therefore sin 67° + cos 75° = cos 23° + sin 15°.
sin 67° + cos 75° = cos 23° + sin 15°, where 23° and 15° lie between 0° and 45°.
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