Find the value of sin 75° sin 15° + cos 75° cos 15°
1. \(\frac {\sqrt3 + 1}{2}\)
2. \(\frac {1}{2}\)
3. 1
4. 0
1. \(\frac {\sqrt3 + 1}{2}\)
2. \(\frac {1}{2}\)
3. 1
4. 0
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Correct Answer – Option 2 : \(\frac {1}{2}\)
Concept:
cos x cos y – sin x sin y = cos (x + y)
cos x cos y + sin x sin y = cos (x – y)
Calculation:
Here, we have to find the value of sin 75° sin 15° + cos 75° cos 15°
As we know that, cos x cos y + sin x sin y = cos (x – y)
∴ sin 75° sin 15° + cos 75° cos 15° = cos 75° cos 15° + sin 75° sin 15°
= cos (75° – 15°)
= cos 60°
= \(\frac {1}{2}\)