document.write( "Question 1193330: If sinA = cosB, compute csc(A+B). \n" ); document.write( "
Algebra.Com's Answer #825357 by math_tutor2020(3817) ![]() You can put this solution on YOUR website! \n" ); document.write( "Answer: 1\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Reason:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "If A+B = 90, then cos(A) = sin(B), and vice versa. \n" ); document.write( "We can also say sin(A) = cos(B) when A+B = 90. \n" ); document.write( "This can be visually proven by drawing out a right triangle with acute angles A and B. I'll leave this proof for the student to carry out.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Therefore, \n" ); document.write( "csc(A+B) = 1/sin(A+B) = 1/sin(90) = 1/1 = 1 \n" ); document.write( " \n" ); document.write( " |