document.write( "Question 1170774: How to prove
\n" ); document.write( "1.sinθ = cosθ tanθ
\n" ); document.write( "2. 1/cosθ=tanθ/sinθ\r
\n" ); document.write( "\n" ); document.write( "3. cos2 θ tan2 θ = sin2 θ
\n" ); document.write( "4. sinθtanθ + cosθ =1/cosθ\r
\n" ); document.write( "\n" ); document.write( "5. sinθ(1 + tanθ) = tanθ(sinθ + cosθ) \n" ); document.write( "

Algebra.Com's Answer #795664 by math_helper(2461) $\"\"$ $\"About$

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1.sin(θ) = cos(θ) tan(θ)\r
\n" ); document.write( "\n" ); document.write( "Start with tan(θ) = sin(θ)/cos(θ), then multiply both sides by cos(θ)\r
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\n" ); document.write( "\n" ); document.write( "2. 1/cos(θ)=tan(θ)/sin(θ)\r
\n" ); document.write( "\n" ); document.write( "Start with tan(θ) = sin(θ)/cos(θ), then divide both sides by sin(θ)
\r
\n" ); document.write( "\n" ); document.write( "3. $\"cos%5E2%28theta%29+tan%5E2%28theta%29+=+sin%5E2%28theta%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "Starting with
\n" ); document.write( "tan(θ) = sin(θ)/cos(θ) \r
\n" ); document.write( "\n" ); document.write( "we get:
\n" ); document.write( " $\"+tan%5E2%28theta%29+=+sin%5E2%28theta%29%2Fcos%5E2%28theta%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "Next just multiply both sides by $\"+cos%5E2%28theta%29+\"$
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\r
\n" ); document.write( "\n" ); document.write( "4. sin(θ)tan(θ) + cos(θ) = 1/cos(θ)\r
\n" ); document.write( "\n" ); document.write( "Using
\n" ); document.write( "tan(θ) = sin(θ)/cos(θ) \r
\n" ); document.write( "\n" ); document.write( "Re-write LHS of given equation (#4) as
\n" ); document.write( "= sin(θ)*sin(θ)/cos(θ) + cos(θ)\r
\n" ); document.write( "\n" ); document.write( "Put both terms over cos(θ):
\n" ); document.write( "= $\"+sin%5E2%28theta%29%2Fcos%28theta%29+%2B+cos%5E2%28theta%29%2Fcos%28theta%29+\"$

\n" ); document.write( "= $\"+%28sin%5E2%28theta%29+%2B+cos%5E2%28theta%29%29+%2F+cos%28theta%29+\"$
\r
\n" ); document.write( "\n" ); document.write( "Noting that $\"+%28sin%5E2%28theta%29+%2B+cos%5E2%28theta%29%29+=+1+\"$ :
\r
\n" ); document.write( "\n" ); document.write( "= $\"+1%2Fcos%28theta%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "

\n" ); document.write( "I leave #5 for you to do, there are enough examples here. As a hint: start with the LHS, multiply thru by sin(θ) then factor out tan(θ). \r
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