Question

SOLVE THIS NO T i m e p a s s
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Answer 1

Step-by-step explanation:

refer to the attachment.

hii mod bhaiya.

Answer 2

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

• $\frac{1}{ \sin( \alpha ) {}^{ \frac{2}{3} }. \cos( \alpha ) {}^{ \frac{2}{3} } }$
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i hope it helps ✅✅✅you