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  4. The general solution of the equation 2 cos 2x+1=3.2- sin x is

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Q. The general solution of the equation $ {{2}^{\cos \,2x}}+1={{3.2}^{-\sin \,x}} $ is

J & K CETJ & K CET 2004

Solution:

Given equation is $ {{2}^{\cos \,2x}}+1={{3.2}^{-\sin \,x}} $ By taking option [a] Let $ x=n\pi $ When $ n=1,\,\,x=\pi $
$ \therefore $ $ {{2}^{\cos \,2\pi }}+1={{3.2}^{-\sin \,x}} $
$ \Rightarrow $ $ 2+1={{3.2}^{0}}\,\,\Rightarrow 3=3 $ When $ n=2,\,x=2\pi $
$ \therefore $ $ {{2}^{\cos \,4\pi }}+1={{3.2}^{-\sin \,2\pi }} $
$ \Rightarrow $ $ {{2}^{1}}+1={{3.2}^{0}} $
$ \Rightarrow $ $ 3=3 $ Hence, option is correct.