Math, asked by arpita63880, 11 months ago

Please answer it.
it's urgent

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prakharverma05parxx3: im not able to post. my amswer

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Answered by mikasa02
1
there is your answer

bas A ki place par theta h
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Answered by Anonymous
3

HEYA \:  \\  \\ GIVEN \:  \: QUESTION \:  \: Is \:  \:  \\  \\  \frac{ \tan(x) }{1 +  \sec(x) }   -  \frac{ \tan(x) }{1 -  \sec(x) }   = 2 \csc(x)  \\  \\ lhs \\  \\  \frac{ \tan(x) }{1 +  \sec(x) }  -  \frac{ \tan(x) }{1 -  \sec(x) }  \\  \\ replace \:  \:  \tan(x)  \: by \:  \frac{ \sin(x) }{ \cos(x) }  \: \:  \:  and \:  \\ replace \:  \sec(x)   \: \: by \:   \: \frac{1}{ \cos(x) }  \\  \\  \\  \frac{  \frac{ \sin(x) }{ \cos(x) } }{1 +  \frac{1}{ \cos(x) } }  \:  -  \:  \frac{  \frac{ \sin(x) }{ \cos(x) }  }{1 -  \frac{1}{ \cos(x) } }  \\  \\  \\  \frac{  \frac{ \sin(x) }{ \cos(x) }  }{ \frac{ \cos(x)  + 1}{ \cos(x) }  }  \:  -  \:  \frac{ \frac{ \sin(x) }{ \cos(x) } }{ \frac{ \cos(x) - 1 }{ \cos(x) } }  \\  \\  \\  \frac{ \sin(x) }{ \cos(x) + 1 }  \:  -  \:  \frac{ \sin(x) }{ \cos(x)  - 1}  \\  \\  \\   \\  \frac{ \sin(x)  \cos(x)  -  \sin(x) -  \sin(x )  \cos(x)  -  \sin(x)  }{ \cos {}^{2} (x) - 1 {}^{2}  }  \\  \\  \\   \frac{ - 2 \sin(x) }{ -  \sin {}^{2} (x) }  \\  \\  \\  \frac{2}{ \sin(x) }  \\  \\  = 2 \csc(x)  \:  \:  \: hence \:  \: proved \\  \\  \\  note \:  \:  \:  \:  \:  \:  \\ here \:  \:  \: a \:  = x

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