A) 0
B) 1
C) 2
D) 4
Correct Answer: B
Solution :
\[si{{n}^{6}}\theta +\text{ }co{{s}^{6}}\theta ~+3si{{n}^{2}}~\theta eco{{s}^{6}}\theta \] \[{{(si{{n}^{2}}\theta )}^{3}}+\text{ }{{(co{{s}^{2}}\theta )}^{3}}+\text{ }3si{{n}^{3}}\theta ~co{{s}^{2}}\theta \] \[(si{{n}^{2}}\theta ~+co{{s}^{2}}\theta )\] \[[~\therefore {{\left( a+b \right)}^{3}}={{a}^{3}}+{{b}^{3}}+3ab\left( a+b \right)]\] Here, \[a=\text{ }si{{n}^{2}}\theta \]and \[b\text{ }=\text{ }co{{s}^{2}}\theta \] \[{{(si{{n}^{2}}\theta ~+co{{s}^{2}}\theta )}^{3}}\] \[(\therefore si{{n}^{2}}\theta ~+\text{ }co{{s}^{2}}\theta =1)={{\left( 1 \right)}^{3}}=[\mathbf{1}]\]
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