Question:
Find the value of sin6 15° + sin6 75° + 6sin2 15° + sin2 75°/sin4 15° + sin4 75° + 5sin2 15° sin2 75°.
Find the value of sin6 15° + sin6 75° + 6sin2 15° + sin2 75°/sin4 15° + sin4 75° + 5sin2 15° sin2 75°.
Updated On: Aug 9, 2024
- sin 15°+sin 75°
- 6/5
- 1
- sin 15°+cos 15°
- None of the above
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The Correct Option is C
Solution and Explanation
Let a = sin2 15°
b = sin2 75° = sin2 (90° - 15°) = cos2 15°
. So, a + b = 1.
Thus,
sin6 15° + sin6 75° + 6sin2 15° + sin2 75°/sin4 15° + sin4 75° + 5sin2 15° sin2 75° =a3+b3+6ab/a2+b2+5ab
= (a+b)(a2+b2-ab) + 6ab/(a+b)2 + 3ab
= (a+b)((a+b)2 - 3ab) + 6ab/(a+b)2 + 3ab using a + b = 1
= -3ab +6ab/3ab
= 1
Hence, option C is the correct answer.
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