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Question Number 68353 by mhmd last updated on 09/Sep/19

If sin x+sin^2 x=1, then value of  cos^2 x+cos^4 x  is

$$\mathrm{If}\:\mathrm{sin}\:{x}+\mathrm{sin}^{\mathrm{2}} {x}=\mathrm{1},\:\mathrm{then}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{cos}^{\mathrm{2}} {x}+\mathrm{cos}^{\mathrm{4}} {x}\:\:\mathrm{is} \\ $$

Answered by $@ty@m123 last updated on 09/Sep/19

Given , 1−sin^2 x=sin x  cos^2 x=sin x   ....(1)  ∴ cos^2 x+cos^4 x    =sin x+sin^2 x=1

$${Given}\:,\:\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} {x}=\mathrm{sin}\:{x} \\ $$$$\mathrm{cos}\:^{\mathrm{2}} {x}=\mathrm{sin}\:{x}\:\:\:....\left(\mathrm{1}\right) \\ $$$$\therefore\:\mathrm{cos}^{\mathrm{2}} {x}+\mathrm{cos}^{\mathrm{4}} {x}\:\: \\ $$$$=\mathrm{sin}\:{x}+\mathrm{sin}^{\mathrm{2}} {x}=\mathrm{1} \\ $$

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