Question
Download Solution PDFWhat is the value of sin 75° + sin 15°?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
sin 75° + sin 15°
Concept used:
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
Calculation:
sin 75° + sin 15°
⇒ sin (90° - 15°) + sin 15°
⇒ cos 15° + sin 15°
⇒ sin 15° + cos 15° = k (let)
According to the concept,
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 =
∴ The value of sin 75° + sin 15° is
Shortcut Trick
We know, sin C + sin D =
sin 75° + sin 15 =
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