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Question Number 174069 by alcohol last updated on 24/Jul/22

Commented by alcohol last updated on 24/Jul/22

please help me

$${please}\:{help}\:{me}\: \\ $$

Answered by aleks041103 last updated on 24/Jul/22

1.  2arcsin((√x))−(π/2)=2t−(π/2)  sin(2t−π/2)=−cos(2t)  ⇒−cos(2t)=2sin^2 t−1=2((√x))^2 −1=2x−1  ⇒Q.E.D

$$\mathrm{1}. \\ $$$$\mathrm{2}{arcsin}\left(\sqrt{{x}}\right)−\frac{\pi}{\mathrm{2}}=\mathrm{2}{t}−\frac{\pi}{\mathrm{2}} \\ $$$${sin}\left(\mathrm{2}{t}−\pi/\mathrm{2}\right)=−{cos}\left(\mathrm{2}{t}\right) \\ $$$$\Rightarrow−{cos}\left(\mathrm{2}{t}\right)=\mathrm{2}{sin}^{\mathrm{2}} {t}−\mathrm{1}=\mathrm{2}\left(\sqrt{{x}}\right)^{\mathrm{2}} −\mathrm{1}=\mathrm{2}{x}−\mathrm{1} \\ $$$$\Rightarrow{Q}.{E}.{D} \\ $$

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