A) \[\sin x=|\sin y|\]
B) \[\sin x=2\sin y\]
C) \[2|\sin x|=3\sin y\]
D) \[2\sin x=\sin y\]
Correct Answer: A
Solution :
\[{{2}^{\sqrt{{{\sin }^{2}}x-2\sin x+5}}}{{.4}^{-{{\sin }^{2}}y}}\le 1\] \[\Rightarrow \]\[{{2}^{\sqrt{{{(\sin x-1)}^{2}}+4}}}\le {{2}^{2{{\sin }^{2}}y}}\] \[\Rightarrow \]\[\sqrt{{{(sinx-1)}^{2}}+4}\le 2{{\sin }^{2}}y\] \[\Rightarrow \]\[{{2}^{\sqrt{{{(sinx-1)}^{2}}+4}}}\le {{2}^{2{{\sin }^{2}}y}}\] \[\Rightarrow \]\[\sqrt{{{(sinx-1)}^{2}}+4}\le 2{{\sin }^{2}}y\] \[\Rightarrow \]\[\sin x=1\]and\[|\sin y|=1\]
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