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Question : 90 of 150
Marks:
+1,
-0
Solution:
Here,
sin‌x+sin‌5x=sin‌3xWe know that,
‌sin‌A+sin‌B=2sin‌‌‌cos‌∴‌‌sin‌x+sin‌5x=sin‌3x⇒2sin‌(‌)‌cos(‌)=sin‌3x⇒2sin‌3x‌cos‌2‌x=sin‌3x∴ Either,
sin‌3x=0 or
2‌cos‌2‌x−1=0sin‌3x=sin‌0‌ or ‌cos‌2‌x=‌=cos‌Comparing obtained equation with standard equation, we have
3x‌=nπ‌ or ‌2x=2mπ±‌∴‌‌x‌=‌‌ or ‌x=mπ+‌,‌ where ‌m,n∈Zx‌=‌,‌
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