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Question : 12 of 160
Marks:
+1,
-0
Solution:
Given,
sin‌2x+bsin‌x+c=0 and
α+β=‌Let
y=sin‌x, thus we get
y2+by+c=0The roots of this equation are
sin‌α and
sin‌β.
So, sum of the roots
=sin‌α+sin‌β=−‌Product of the roots
=sin‌α⋅sin‌β=cSince,
α+β=‌⇒‌‌β=‌−αSo,
sin‌α+sin‌(‌−α)=−b‌⇒sin‌α+cos‌α=−b‌⇒(∵sin‌α+cos‌α)2=(−b)2‌⇒sin‌2α+cos2α+2sin‌α‌cos‌α=(−b)2‌⇒1+2c=b2[∵sin‌2θ+cos2θ=1]‌⇒b2−1=2c
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