Question 757559
5 tanx cos^2x -3sin^2x =0
{{{5tan(x)cos^2(x)-3sin^2(x)=0}}}
{{{(5sin(x)/cos(x))cos^2(x)-3sin^2(x)=0}}}
{{{5sin(x)cos(x)-3sin^2(x)=0}}}
{{{sin(x)(5cos(x)-3sin(x))=0}}}
sin(x)=0
x=0
or
{{{5cos(x)-3sin(x)=0}}}
{{{5sqrt(1-sin^2(x))=3sin(x)}}}
{{{25(1-sin^2(x))=9sin^2(x)}}}
{{{25-25sin^2(x))=9sin^2(x)}}}
{{{25-34sin^2(x))=0}}}
{{{sin^2(x)=25/34}}}
sin(x)=5/√34
x≈59.04º