Выносим за скобки 4 в меньшей степени 2х+3
![4 ^{2x+3}(4 ^{2x+5-2x-3}+1+3\cdot 4 ^{2x+4-2x-3} =116, \\ 4 ^{2x+3}(4 ^{2}+1+3\cdot 4 ^{1} )=116, \\ 4 ^{2x+3}\cdot 29=116, \\ 4 ^{2x+3}=4,](https://tex.z-dn.net/?f=4+%5E%7B2x%2B3%7D%284+%5E%7B2x%2B5-2x-3%7D%2B1%2B3%5Ccdot+4+%5E%7B2x%2B4-2x-3%7D+%3D116%2C++%5C%5C+4+%5E%7B2x%2B3%7D%284+%5E%7B2%7D%2B1%2B3%5Ccdot+4+%5E%7B1%7D+%29%3D116%2C+%5C%5C+4+%5E%7B2x%2B3%7D%5Ccdot+29%3D116%2C+%5C%5C+4+%5E%7B2x%2B3%7D%3D4%2C+++++++++)
2x+3=1
2x=-2
x=-1
Sin 2x+2cos 2x =1
2sinxcosx+2(cosx)^2-2(sinx)^2-(cosx)^2-(sinx)^2=0
2sinxcosx+(cosx)^2-3(sinx)^2=0 |:(cosx)^2 не=0
2tgx+1-3(tgx)^2=0|*(-1) x не=П/2+Пn,n принадлежит Z
3(tgx)^2-2tgx-1=0 |tgx=t
3t^2-2t-1=0
D=(-2)^2-4*3*(-1)=16
t1=(2+4)/6=1 t2=(2-4)/6=-1/3
tgx=1 tgx=-1/3
<span>x=П/4+Пn,n принадлежит Z x=-arctg 1/3 + Пk,k принадл. Z
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