I am not sure how khổng lồ solve this: \$\$sin^2 (2x) = 2 sin (2x)\$\$I thought I could rewrite it lượt thích this: \$\$4 sin^2 (x) cos^2 (x) = 4 sin (x) cos (x)\$\$and maybe lượt thích this as well: \$\$ sin (x) cos (x) = 0\$\$

but I have no idea whether it is correct và how get lớn the solution ..

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thanks for help  HINT:

Let \$sin(2x)=t\$ & you get a quadratic equation in \$t\$.

You need lớn calculate roots of, \$t^2-2t=0\$. \$\$sin^2(2x) = 2sin(2x)\$\$Assign a variable khổng lồ \$sin(2x)\$ to lớn get a simple quadratic equation.\$\$t = sin(2x)\$\$Rewrite the equation.\$\$t^2 = 2t\$\$Now, just solve sầu the equation.\$\$t^2-2t = 0 implies t(t-2) = 0 implies t = 0 ext OR t = 2\$\$Plug in \$sin(2x)\$.For \$n in igbiglands.combbZ\$, we get the following solutions:\$\$t = 0 implies sin(2x) = 0 implies 2x = (sin^-1 0)+2pi n\$\$

\$\$implies egincases2x = 2pi n implies oxedx = pi n\\2x = pi+2pi nimplies oxedx = fracpi2+pi n\endcases\$\$We can immediately rule out the second option (\$t = 2\$) because the range of \$sin x\$ is \$y in <-1, 1>\$.

Combining the two solutions, we can reach a single general solution: \$\$oxedx = fracnpi2\$\$ HINT

We have

\$\$sin^2 (2x) = 2 sin (2x)iff sin^2 (2x) - 2 sin (2x)=0 iff sin (2x)cdot =0\$\$

then reCall that

\$\$Acdot B=0 iff A=0 ,lor,B=0\$\$ Thanks for contributing an answer to bigbiglands.comematics Staông xã Exchange!

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