Question Number 37110 by mondodotto@gmail.com last updated on 09/Jun/18
$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\left(\boldsymbol{\mathrm{cos}\vartheta}−\boldsymbol{\mathrm{sin}\vartheta}\right)^{\mathrm{2}} +\left(\boldsymbol{\mathrm{cosec}\vartheta}+\boldsymbol{\mathrm{sin}\vartheta}\right)^{\mathrm{2}} =\mathrm{2} \\ $$
Commented by tanmay.chaudhury50@gmail.com last updated on 09/Jun/18
$${to}\:{make}\:{it}\:{true}\:{replace}\:{cosec}\theta\:{by}\:{cos}\theta \\ $$
Commented by candre last updated on 09/Jun/18
$$\vartheta=\pi/\mathrm{2} \\ $$$$\left(\mathrm{cos}\:\vartheta−\mathrm{sin}\:\vartheta\right)^{\mathrm{2}} +\left(\mathrm{cosec}\:\vartheta+\mathrm{sin}\:\vartheta\right)^{\mathrm{2}} = \\ $$$$\left(\mathrm{0}−\mathrm{1}\right)^{\mathrm{2}} +\left(\mathrm{1}+\mathrm{1}\right)^{\mathrm{2}} =\mathrm{1}+\mathrm{4}=\mathrm{5} \\ $$$$\mathrm{are}\:\mathrm{you}\:\mathrm{sure}\:\mathrm{question}\:\mathrm{is}\:\mathrm{right}? \\ $$
Answered by MJS last updated on 09/Jun/18
$$\mathrm{it}'\mathrm{s}\:\mathrm{not}\:\mathrm{true} \\ $$