Question 804658
tan x + cot x = 25/12 , find sin x + cos x
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{{{tan(x)+cot(x)=25/12}}}
{{{tan(x)+(1/tan(x))=25/12}}}
{{{(tan^2(x)+1)/tan(x)=25/12}}}
{{{(12tan^2(x)+12)=25tan(x)}}}
{{{12tan^2(x)-25tan(x)+12=0}}}
(4tan(x)-3)(3tan(x)-4)
..
tan(x)=3/4
working with (3-4-5) right triangle
sin(x)=3/5
cos(x)=4/5
sin(x)+cos(x)=3/5+4/5=7/5
or
tan(x)=4/3
working with (3-4-5) right triangle
sin(x)=4/5
cos(x)=3/5
sin(x)+cos(x)=4/5+3/5=7/5