Math, asked by prashant247, 3 months ago

SOLVE THIS NO T i m e p a s s
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Answers

Answered by SugaryHeart
9

Step-by-step explanation:

refer to the attachment.

hii mod bhaiya.

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Answered by diwanamrmznu
10

given★:-

m =  \cosec( \alpha )  -  \sin( \alpha )

and

n =  \sec( \alpha ) -  \cos( \alpha )

FIND★:-

m {}^{ \frac{2}{3} }  + n {}^{ \frac{2}{3} }  =  {?} \\

EVALUTION★:-

  • We know that

  •  =  >  \cosec( \alpha )  =  \frac{1}{sin( \alpha )}  ..(1
  •  =  > m = cosec( \alpha ) - sin( \alpha )
  • put eq (1 value
  •  =  > m =  \frac{1}{ \sin( \alpha ) }  -  \sin( \alpha )   \\  \\  =  \frac{1 -  \sin {}^{2} ( \alpha ) }{ \sin( \alpha ) }
  • we know that

  • 1 -  \sin {}^{2} ( \alpha )  =  \cos {}^{2} ( \alpha )

 =  \frac{ \cos {}^{2} ( \alpha ) }{ \sin( \alpha ) } ..(2 \\

 =  > n =  \sec( \alpha )  -  \cos( \alpha )

we know that

  •  =  >  \sec( \alpha )  =  \frac{1}{ \cos( \alpha ) } \\
  • to

  • n =  \frac{1}{ \cos( \alpha ) }   -  \cos( \alpha )  \\  \\  =  \frac{1 -  \cos {}^{2} ( \alpha ) }{ \cos( \alpha ) }
  • we know that

  •  =  > 1 -  \cos {}^{2} ( \alpha )   =  \sin {}^{2} ( \alpha )

 n =  \frac{ \sin {}^{2} ( \alpha ) }{ \cos( \alpha ) }   ..(3 \\

  • put m and n value

 = m {}^{ \frac{2}{3} }  + n {}^{ \frac{2}{3} }  \\  \\  \\ ( \frac{ \cos {}^{2} ( \alpha ) }{ \sin( \alpha ) } ) {}^{ \frac{2}{3} }  + (  \frac{ \sin {}^{2} ( \alpha ) }{cos( \alpha )} ) {}^{ \frac{2}{3} }  \\  \\  \\  =  \frac{ \cos( \alpha ) {}^{2 \times  \frac{2}{3} }  }{ \sin {}^{ \frac{2}{3} } ( \alpha ) }  +   \frac{ \sin {}^{2 \times  \frac{2}{3} } ( \alpha ) }{ \cos \frac{2}{3} ( \alpha ) }  \\  \\  \\ =   \frac{ \cos {}^{2} ( \alpha ) +  \sin {}^{2} ( \alpha )  }{ \sin {}^{ \frac{2}{3} } ( \alpha )  \cos {}^{ \frac{2}{3} }  ( \alpha )  } \\  \\   \\

we know that

  •  \sin {}^{2} ( \alpha )  +  \cos {}^{2} ( \alpha )  = 1
  • answer

  •  \frac{1}{ \sin( \alpha ) {}^{ \frac{2}{3} }. \cos( \alpha )  {}^{ \frac{2}{3} }     } \\
  • ==============================

i hope it helps ✅✅✅you

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