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Solve:
\n" ); document.write( "cos-¹ x + cos-¹ 2x = 60°
\n" ); document.write( "**
\n" ); document.write( "cos A=x
\n" ); document.write( "sin A=√(1-x^2)
\n" ); document.write( "cos B=2x
\n" ); document.write( "sin B=√(1-4x^2)
\n" ); document.write( "Using Trig Identity: cos(A+B)=cos A*cos B-Sin A*Sin B
\n" ); document.write( "cos(A+B)=x*2x-(√(1-x^2)*√(1-4x^2)=cos 60º=1/2
\n" ); document.write( "cos(A+B)=2x^2-(1-5x^2+4x^4)=1/2
\n" ); document.write( "2x^2-1+5x^2-4x^4=1/2
\n" ); document.write( "-1+7x^2-4x^4-1/2=0
\n" ); document.write( "4x^4-7x^2+3/2=0
\n" ); document.write( "8x^4-14x^2+3=0
\n" ); document.write( "let u=x^2
\n" ); document.write( "u^2=x^4
\n" ); document.write( "8u^2-14u+3=0
\n" ); document.write( "(4u-1)(2x-3)=0
\n" ); document.write( "u=1/4
\n" ); document.write( "or
\n" ); document.write( "u=3/2
\n" ); document.write( "..
\n" ); document.write( "1/4=x^2
\n" ); document.write( "x=±1/2
\n" ); document.write( "arccos (-1/2)+arccos (2*-1/2)=-60º+180≠60º (reject)
\n" ); document.write( "arccos (1/2)+arccos (2*1/2)=60º+arccos(1)=60º+0=60º (answer)
\n" ); document.write( "..
\n" ); document.write( "3/2=x^2
\n" ); document.write( "x=±√(3/2)=1.2247 (reject, (0 ≤ cosx ≤1))
\n" ); document.write( "..\r
\n" ); document.write( "\n" ); document.write( "ans:
\n" ); document.write( "x=1/2 \n" ); document.write( "