document.write( "Question 792275: prove that 15tan^2 +4sec^2 = 23 \n" ); document.write( "

Algebra.Com's Answer #479904 by lwsshak3(11628) $\"\"$ $\"About$

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prove that 15tan^2(x) +4sec^2(x) = 23
\n" ); document.write( "solve for x:
\n" ); document.write( " $\"15+tan%5E2%28x%29%2B4sec%5E2%28x%29=23\"$
\n" ); document.write( " $\"15+%28sin%5E2%28x%29%2Fcos%5E2%28x%29%29%2B%284%2Fcos%5E2%28x%29%29=23\"$
\n" ); document.write( " $\"%2815+sin%5E2%28x%29%2B4%29%2F%28cos%5E2%28x%29%29=23\"$
\n" ); document.write( " $\"15+sin%5E2%28x%29%2B4=23+cos%5E2%28x%29\"$
\n" ); document.write( " $\"15+sin%5E2%28x%29%2B4=23%281-sin%5E2%28x%29%29\"$
\n" ); document.write( " $\"15+sin%5E2%28x%29%2B4=23-23sin%5E2%28x%29\"$
\n" ); document.write( " $\"38+sin%5E2%28x%29=19\"$
\n" ); document.write( "sin^2(x)=19/38=1/2
\n" ); document.write( "sin(x)=√1/√2
\n" ); document.write( "x=π/4
\n" ); document.write( "Check:
\n" ); document.write( "15tan^2(x)=15tan^2(π/4)15*1=15
\n" ); document.write( "4sec^2(x)=4/cos^2(π/4)=4/(1/2)=8
\n" ); document.write( "15tan^2(x)+15tan^2(x)=15+8=23
\n" ); document.write( "Given identity is true if x=π/4 \n" ); document.write( "

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