Math, asked by mamtaraj8988, 8 months ago

Cosec A÷Cosec A-1+(Cosec A÷Cosec A+1

Answers

Answered by Anonymous
44

Correct Question :

  • Prove cosec A / cosec A-1 + cosec A / cosec A + 1 = 2 sec² A

Solution :

→ cosec A / cosec A - 1 + cosec A / cosec A + 1

→ cosec A ( cosec A + 1+cosec A - 1 /cosec² A - 1 )

→ cosec A ( 2 cosec A / cot² A )

→ 2 cosec² A / cot² A

→ 2 × 1/sin² A ( sin² A / cos² A )

→ 2 / cos² A

→ 2 sec² A

LHS = RHS

Hence proved


mysticd: Use = symbol instead of implies
Answered by Anonymous
387

Correct question :

 \frac{Prove \:  cosec  \: A}{cosec  \: A - 1}    +  \frac{cosec  \: A}{cosec \:  A + 1}  = 2  {sec}^{2}  A

Calculation :

 \frac{cosec \: A}{cosec \:  A - 1}   + \frac{cosec \: A}{cosec \:  A  +  1}  \\  = cosec \: A  \: (\frac{cosec A + 1 + cosec A - 1}{cosec  \: A  + 1})  \\  = cosec  \: A \:  (\frac{2  \: cosec  A}{ {cot}^{2}A }) \\  =  \frac{2  \:  {cosec}^{2}  A}{{cot}^{2}  A}   \\  =  \frac{2 \times 1}{ {sin}^{2} \:A  } ( \frac{ {sin}^{2}A }{ {cos}^{2}A })  \\  =  \frac{2}{ {cos}^{2}A }  \\  = 2 \:  {sec}^{2} A

LHS = RHS

Hence proved


mysticd: Under calculation second line denominator is incomplete . Please edit
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