Question

1 / cosec A - cot A - 1 / sin A = 1 / sin A - 1 cosec A + cot A

Answer 1

LHS = 1/cosec A - cot A - 1/ sin A
= 1/cosec A - cot A * cosec A + cot A/cosec A + cot A - 1/sin A
= (cosec A + cot A)/(cosec^2A - cot^2A) - 1/sin A
= (cosec A + cot A)/(cosec^2A - cot^2A) - cosec A
= cosec A + cot A - cosec A
= cot A.

RHS = 1/sin A - 1/cosecA+cotA
= cosecA - (cosecA - cotA)/(cosec^2A - cot^2A)
= cosec A - (cosec A - cot A)
= cosec A - cosec A + cot A
= cot A.
LHS = RHS.

Answer 2

Answer:

Hey buddy, here is ur answer !!

Step-by-step explanation:

We have ,

LHS :   1 / cosec A- cot A - 1 / sin A

       =  1 / ( cosec A - cot A ) x ( cosec A + cot A ) / (cosec A + cot A ) - 1 / sin A

         

       =  cosec A + cot A / ( $cosec^{2} A + cot^{2} A$ )   - cosec A

         

       =  cosec A + cot A - cosec A

[ LHS : cot A ]............................................( i )

and,  

RHS : 1 / sin A - 1 / cosec A + cot A

         =  1 / sin A - cosec A - cot A  / ( cosec A + cot A )( cosec A - cot A )

   

         =   1 / sin A -  cosec A - cot A / $cosec^{2} A - cot^{2} A$

         =    cosec A - (  cosec A - cot A )

[ RHS : cot A ].............................................( ii )

From i and ii we find that LHS=RHS

Hope it helps ,

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