document.write( "Question 35670: If angles A, B, and C are the sides of a triangle such that sin(A+B)=1/cosC and cos(A+B)=cosC, then show that the triangle is a right triangle. \n" ); document.write( "
Algebra.Com's Answer #21845 by venugopalramana(3286)\"\" \"About 
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\n" ); document.write( "> If angles A, B, and C are the sides of a triangle such that sin(A+B)=1/cosC
\n" ); document.write( "> and cos(A+B)=cosC, then show that the triangle is a right triangle.
\n" ); document.write( "> SINCE IN A TRIANGLE A+B+C=180
\n" ); document.write( "SIN(A+B)=SIN(180-C)=SIN(C)=1/COS(C)
\n" ); document.write( "HENCE SIN(C)*COS(C)=1.......SIN(2C)/2=1......SIN2C=2....WRONG...IT MUST BE
\n" ); document.write( "SIN(A+B)=1-COSC...OR...=1
\n" ); document.write( "THEN SIN(C)=1-COS(C)
\n" ); document.write( "SIN(C)+COS(C)=1...DIVIDE THROUGHOUT BY SQRT(2)
\n" ); document.write( "SIN(C)/SQRT(2)+COS(C)/SQRT(2)=1/SQRT(2).......
\n" ); document.write( "PUT SIN(45)=COS(45)=1/SQRT(2)
\n" ); document.write( "SIN(C)COS(45)+COS(C)SIN(45)=SIN(45)
\n" ); document.write( "SIN(45+C)=SIN(45)=SIN(180-45)=SIN(135)
\n" ); document.write( "45+C=135
\n" ); document.write( "C=90...RIGHT ANGLED TRIANGLE.\r
\n" ); document.write( "\n" ); document.write( "COS(A+B)=COS(180-C)=-COS(C)=COS(C)...GIVEN
\n" ); document.write( "COS(C)=0...OR....C=90..RIGHT ANGLED TRIANGLE
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