Math, asked by joshibani, 5 hours ago

1+sinA- cosA/1+sinA+cosA= √1-cosA/1+cosA pls answe fast and correctly the first will be marked brainliest

Answers

Answered by sandy1816
0

LHS

 \frac{1 + sina - cosa}{1 + sina + cosa}  \\  \\  =  \frac{ \frac{1 + sina - cosa}{sina} }{ \frac{1 + sina + cosa}{sina} }  \\  \\  =  \frac{coseca - cota + 1}{coseca + cota + 1}  \\  \\  =  \frac{(coseca - cota) + ( {cosec}^{2}a -  {cot}^{2}  a)}{coseca + cota + 1}  \\  \\  =  \frac{(coseca - cota)(1 + coseca + cota)}{(1 + coseca + cota)}  \\  \\  = coseca - cota

RHS

 \sqrt{ \frac{1 - cosa}{1 + cosa} }  \\  \\  =  \sqrt{ \frac{1 - cosa}{1 + cosa} \times  \frac{1 - cosa}{1 - cosa}  }  \\  \\  =  \sqrt{ \frac{( {1 - cosa})^{2} }{1 -  {cos}^{2} a} }  \\  \\  =  \sqrt{ \frac{( {1 - cosa})^{2} }{ {sin}^{2} a} }  \\  \\  =  \frac{1 - cosa}{sina}  \\  \\  = coseca - cota

 \therefore \:  LHS = RHS

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