Question
Download Solution PDFFind the value of (sin 75° + sin 15°).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Find the value of (sin 75º + sin 15º)
Formula used:
sin(A + B) = sinA cosB + cosA sinB
Calculation:
sin 75º = sin(45º + 30º)
⇒ sin 45º cos 30º + cos 45º sin 30º
⇒ (√2/2) × (√3/2) + (√2/2) × (1/2)
⇒ (√6/4) + (√2/4)
sin 15º = sin(45º - 30º)
⇒ sin 45º cos 30º - cos 45º sin 30º
⇒ (√2/2) × (√3/2) - (√2/2) × (1/2)
⇒ (√6/4) - (√2/4)
sin 75º + sin 15º
⇒ (√6/4 + √2/4) + (√6/4 - √2/4)
⇒ (√6/4) + (√6/4)
⇒ 2(√6/4)
⇒ √6/2
∴ The correct answer is option 1.
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