Question

prove that.............​

Answer 1

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Answer 2

Given : 1/(cosecA - CotA )  - 1/(SinA)   =  1/SinA  - 1/(CosecA + cotA)

To find  : Prove

Solution:

1/(cosecA - CotA )  - 1/(SinA)   =  1/SinA  - 1/(CosecA + cotA)

LHS  =  

1/(cosecA - CotA )  - 1/(SinA)

multiplying numerator & denominator of 1st term with cosecA +  CotA

and using Cosec²A - Cot²A = 1      => CosecA + CotA = 1/(CosecA - CotA)

& 1/SinA = CosecA

= CosecA + CotA  - CosecA

= CosecA  - CosecA + CotA

= CosecA   -  ( CosecA  - CotA)

Using again CosecA + CotA = 1/(CosecA - CotA) => CosecA - CotA  = 1/(CosecA + CotA)    &  CosecA = 1/SinA

= 1/SinA  -   1/(CosecA + CotA)

= RHS

QED

Hence Proved

1/(cosecA - CotA )  - 1/(SinA)   =  1/SinA  - 1/(CosecA + cotA)

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