Question Number 14591 by Tinkutara last updated on 02/Jun/17
Answered by prakash jain last updated on 02/Jun/17
$$\mathrm{For}\:{x}\in\mathbb{R} \\ $$$$\mathrm{cosec}^{\mathrm{2}} {x}\geqslant\mathrm{1} \\ $$$$\mathrm{tan}^{\mathrm{100}} {x}\geqslant\mathrm{0} \\ $$$$\mathrm{for}\:\mathrm{the}\:\mathrm{equality}\:\mathrm{to}\:\mathrm{hold} \\ $$$$\mathrm{cosec}\:{x}=\pm\mathrm{1} \\ $$$$\mathrm{tan}\:{x}=\mathrm{0} \\ $$$$\mathrm{No}\:\mathrm{real}\:\mathrm{solutions} \\ $$
Commented by mrW1 last updated on 02/Jun/17
$${the}\:{question}\:{is}\:{probably}\: \\ $$$$\mathrm{sec}^{\mathrm{100}} \:{x}\:+\:\mathrm{tan}^{\mathrm{100}} \:{x}\:=\:\mathrm{1} \\ $$
Commented by Tinkutara last updated on 03/Jun/17
$$\mathrm{Thanks}\:\mathrm{Sir}!\:\mathrm{The}\:\mathrm{answer}\:\mathrm{is}\:\mathrm{also}\:\mathrm{no} \\ $$$$\mathrm{solutions}\:\mathrm{exist}. \\ $$
Commented by mrW1 last updated on 03/Jun/17
$${if}\:{the}\:{question}\:{is}\: \\ $$$$\mathrm{sec}^{\mathrm{100}} \:{x}\:+\:\mathrm{tan}^{\mathrm{100}} \:{x}\:=\:\mathrm{1} \\ $$$${the}\:{solution}\:{is} \\ $$$$\mathrm{sec}\:{x}=\pm\mathrm{1}\:{and}\:\mathrm{tan}\:{x}=\mathrm{0} \\ $$$$\Rightarrow{x}={n}\pi \\ $$
Commented by Tinkutara last updated on 03/Jun/17
$$\mathrm{Thanks}! \\ $$