sin 75° + sin 15° का मान क्या होगा?

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SSC CGL 2022 Tier-I Official Paper (Held On : 09 Dec 2022 Shift 4)
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SSC CGL Tier 1 2025 Full Test - 01
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दिया गया है:

sin 75° + sin 15°

प्रयुक्त अवधारणा:

1. 2 × sin θ × cos θ = sin 2θ

2. sin (90° - θ) = cos θ

3. sin 30° = 1/2

4. sin2 θ + cos2 θ = 1

गणना:

sin 75° + sin 15°

⇒ sin (90° - 15°) + sin 15°

⇒ cos 15° + sin 15°

⇒ sin 15° + cos 15° = k (माना)

अवधारणा के अनुसार,

sin2 15° + cos2 15° = 1

⇒ (sin 15° + cos 15°)2 - 2.sin 15°.cos 15° = 1

⇒ k2 - sin (2 × 15)° = 1

⇒ k2 - sin 30° = 1

⇒ k2 - 1/2 = 1 

⇒ k2 = 1 + 1/2

⇒ k2 = 3/2

⇒ k = 

 sin 75° + sin 15° का मान है।

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