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AlladinOne [14]
4 years ago
14

Write a problem to represent: 4x-5=11. Identify what the variable represents.

Mathematics
2 answers:
oksano4ka [1.4K]4 years ago
4 0
X=4
4*(x)-5=11
4*(4)-5=11
lorasvet [3.4K]4 years ago
3 0
Your answer is probably:
X= 4
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Prove each of these identities.
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<h3><u>Answer</u><u>:</u></h3>

<u>➲</u><u> </u><u>(</u><u> </u><u>1</u><u> </u><u>+</u><u> </u><u>sec </u><u>x </u><u>)</u><u>(</u><u> </u><u>cosec </u><u>x </u><u>-</u><u> </u><u>cot </u><u>x </u><u>)</u><u> </u><u>=</u><u> </u><u>tan </u><u>x</u>

  • <em>Solving</em><em> </em><em>for </em><em>L.H.S</em>

\implies\quad \sf{(1+sec\:x)(cosec\:x-cot\:x) }

\implies\quad \sf{ \left(1+\dfrac{1}{cos\:x}\right)\left(\dfrac{1}{sin\:x}-\dfrac{cos\:x}{sin\:x}\right)}

\implies\quad \sf{ \left(\dfrac{1+cos\:x}{cos\:x}\right)\left(\dfrac{1-cos\:x}{sin\:x}\right)}

\implies\quad \sf{ \left(\dfrac{1-cos^2 x}{cos\:x.sin\:x}\right)}

\implies\quad \sf{ \left( \dfrac{sin^2 x}{cos\:x.sin\:x}\right)}

\implies\quad \sf{ \left( \dfrac{sin\:x.\cancel{sin\:x}}{cos\:x.\cancel{sin\:x}}\right)}

\implies\quad \sf{\left( \dfrac{sin\:x}{cos\:x}\right) }

\implies\quad\underline{\underline{\pmb{ \sf{tan\:x}}} }

<u>➲</u><u> </u><u>(</u><u> </u><u>1</u><u>+</u><u> </u><u>sec </u><u>x </u><u>)</u><u>(</u><u> </u><u>1</u><u>-</u><u> </u><u>cos </u><u>x </u><u>)</u><u> </u><u>=</u><u> </u><u>sin </u><u>x.</u><u> </u><u>tan </u><u>x</u>

  • <em>Solving </em><em>for </em><em>L.H.S</em>

\implies\quad \sf{ ( 1+ sec\:x)(1-cos\:x)}

\implies\quad \sf{\left(1+\dfrac{1}{cos\:x} \right) \left( 1-cos\:x\right)}

\implies\quad \sf{ \left(\dfrac{cos\:x+1}{cos\:x} \right)(1-cos \:x)}

\implies\quad \sf{\dfrac{1-cos^2 x}{cos\:x} }

\implies\quad \sf{\dfrac{sin^2x}{cos\:x} }

\implies\quad \sf{sin\:x.\left( \dfrac{sin\:}{cos\:x}\right) }

\implies\quad\underline{\underline{\pmb{ \sf{sin\:x.tan\:x}}} }

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