document.write( "Question 1064967: If cos x = sin (20 + x ) degrees and 0 degrees < x < 90 degrees , the value of x is ___ degrees \n" ); document.write( "

Algebra.Com's Answer #680072 by Boreal(15235) $\"\"$ $\"About$

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cos x=sin (20+x)
\n" ); document.write( "sin (a+b)=sin a* cos b+cos a*sin b
\n" ); document.write( "cos x=sin 20*cos x+cos 20*sin x
\n" ); document.write( "cos x-sin20*cos x=cos 20* sin x
\n" ); document.write( "cos x(1-sin 20)=cos 20* sin x
\n" ); document.write( "(1-sin 20)/(cos 20)=sin x/cos x=tan x
\n" ); document.write( "(1-.3420)/0.9397=0.6580/0.9397=.7002
\n" ); document.write( "arc tan (0.7002)=35 degrees
\n" ); document.write( "cos 35=sin (20+x)=0.8192
\n" ); document.write( "arc sin (0.8192)=55 degrees
\n" ); document.write( "sin (20+x)=sin (55 degrees)
\n" ); document.write( "x=35 degrees
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