Question

prove that:
(cosecA - sin A) ( sec A- cosA) ( tanA+cotA)= 1​

Answer 1

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Answer 2

HEY MATE YOUR ANSWER IS HERE...

USING TRIGNOMATERIC RATIOS

$cosec \: a = \frac{1}{sin \: a} \\ \\ sec \: a = \frac{1}{cos \: a} \\ \\ tan \: a \: = \frac{sin \: a}{cos \: a} \\ \\ cot \: a = \frac{cos \: a}{sin \: a}$

NOW BY TAKING LHS

$( \: cosec \: a \: - \: sin \: a)(sec \: a - cos \: a)(tan a\: + cot \: a)$

THEN

$(\frac{1}{sin \: a} - \: sin \: a)( \frac{1}{cos \: a} - cos \: a)( \frac{sin \: a}{cos \: a} + \frac{cos \: a \: }{sn \: a } )$

NOW

$(\frac{1 - {sin}^{2} a}{sin \: a} )( \frac{1 - {cos}^{2} a}{cos \: a} )( \frac{ {sin}^{2}a \: + {cos}^{2} a }{sin a\: \times \: cos \: a } )$

NOW BY TRIGNOMATERIC IDENTITY

1 - SIN² A = COS² A

1 - COS² A= SIN² A

SIN²A + COS² = 1

$( \frac{ {cos \: }^{2} a}{sin \: a} )( \frac{ {sin}^{2}a }{cos \: a} )( \frac{1}{sin \: a \: cos \: a} )$

BY SOLVING IT FURTHER

$( \frac{cos \: a}{1} )( \frac{sin \: a}{1} )( \frac{1}{sin \: a \: cos \: a \: } )$

HENCE

BY SOLVING OUT THE TERMS

WE GET

= 1

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