Question

Prove that root over 1-cosA/1+cosA=cosecA-cotA

Answer 1

Answer:

Hi ,

LHS = sqrt [ ( 1 + cos A ) / ( 1 - cos A )

Multiply numerator and denominator with ( 1 + cos A )

= sqrt [ ( 1 + cos A ) ( 1 + cos A ) / ( 1 - cos A ) ( 1 + cos A ) ]

= sqrt [ ( 1 + cos A ) ^2 / ( 1^2 - cos ^2 A ) ]

[ since ( a + b ) ( a - b ) = a^2 - b ^2 ]

= sqrt [ ( 1 + cos A ) ^2 / ( sin ^2 A ) ]

= ( 1 + cos A ) / sin A

= ( 1 / sin A ) + ( cos A / sin A )

= cosec A + cot A

= RHS

I hope this helps you.

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Answer 2

Please see the image