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Question Number 112466 by Aina Samuel Temidayo last updated on 08/Sep/20

Answered by 1549442205PVT last updated on 08/Sep/20

$$\mid \mathrm{cosx}\mid ⩾1-{\sin }^2\mathrm{x}\iff \mid \mathrm{cosx}\mid ⩾{\cos }^2\mathrm{x}=\mid \mathrm{cosx}{\mid }^2$$$$\iff \mid \mathrm{cosx}\mid ⩽1.\mathrm{The}\mathrm{last}\mathrm{inequality}\mathrm{is}$$$$\mathrm{always}\mathrm{true}\mathrm{\forall }\mathrm{x}.\mathrm{Hence},\mid \mathrm{cosx}\mid ⩾1-{\sin }^2\mathrm{x}$$$$\mathrm{is}\mathrm{true}(\mathbf{q}.\mathbf{e}.\mathbf{d})$$

Commented by Aina Samuel Temidayo last updated on 08/Sep/20

$$\mathrm{Ok}.\mathrm{Thanks}.$$

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