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प्रश्न
Express the following in terms of trigonometric ratios of angles between 0° and 45°.
cos 51° + cot 49° – sec 47°
योग
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उत्तर
Given: cos 51° + cot 49° – sec 47°
Step-wise calculation:
1. Use complementary-angle identities:
cos θ = sin(90° – θ)
cot θ = tan(90° – θ)
sec θ = cosec(90° – θ)
2. cos 51° = sin(90° – 51°) = sin 39°.
3. cot 49° = tan(90° – 49°) = tan 41°.
4. sec 47° = cosec(90° – 47°) = cosec 43°.
5. Substitute: cos 51° + cot 49° – sec 47° = sin 39° + tan 41° – cosec 43°.
cos 51° + cot 49° – sec 47° = sin 39° + tan 41° – cosec 43°, where 39°, 41° and 43° all lie between 0° and 45°.
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