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Question-65749




Question Number 65749 by bshahid010@gmail.com last updated on 03/Aug/19
Answered by Tanmay chaudhury last updated on 03/Aug/19
sin^2 x+sin^4 x+sin^6 x+...∞  =((sin^2 x)/(1−sin^2 x))  =tan^2 x  so e^(tan^2 x) ×ln(2)  now x^2 −9x+8=9  (x−1)(x−8)=0  x=1  or x=8  i have doubt...1) x of tan^2 (x) ← and  x of   x^2 −9x+8=0  ←x of this eqn   are same or not??  2)((cosx)/(sinx+sinx ←look here  both are sinx))  so pls recheck question
$${sin}^{\mathrm{2}} {x}+{sin}^{\mathrm{4}} {x}+{sin}^{\mathrm{6}} {x}+…\infty \\ $$$$=\frac{{sin}^{\mathrm{2}} {x}}{\mathrm{1}−{sin}^{\mathrm{2}} {x}} \\ $$$$={tan}^{\mathrm{2}} {x} \\ $$$${so}\:{e}^{{tan}^{\mathrm{2}} {x}} ×{ln}\left(\mathrm{2}\right) \\ $$$${now}\:{x}^{\mathrm{2}} −\mathrm{9}{x}+\mathrm{8}=\mathrm{9} \\ $$$$\left({x}−\mathrm{1}\right)\left({x}−\mathrm{8}\right)=\mathrm{0} \\ $$$${x}=\mathrm{1}\:\:{or}\:{x}=\mathrm{8} \\ $$$$\left.{i}\:{have}\:{doubt}…\mathrm{1}\right)\:{x}\:{of}\:{tan}^{\mathrm{2}} \left({x}\right)\:\leftarrow\:{and}\:\:{x}\:{of}\: \\ $$$${x}^{\mathrm{2}} −\mathrm{9}{x}+\mathrm{8}=\mathrm{0}\:\:\leftarrow{x}\:{of}\:{this}\:{eqn}\: \\ $$$${are}\:{same}\:{or}\:{not}?? \\ $$$$\left.\mathrm{2}\right)\frac{{cosx}}{{sinx}+{sinx}\:\leftarrow{look}\:{here}\:\:{both}\:{are}\:{sinx}} \\ $$$$\boldsymbol{{so}}\:\boldsymbol{{pls}}\:\boldsymbol{{recheck}}\:\boldsymbol{{question}} \\ $$