Question

$\underline{\huge\mathbb{Trigonometry !}}$


Show that ,

$\frac{cos A - sin A + 1}{cos A + sin A - 1} = cosec A + cot A$ , by using the identity :- [tan]cosec^2A = 1 + cot^2 A[/tex]


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Answer 1

cos- sin+1)/( cos + sin -1)

divide N and D by sin

cot- 1+ cosec)/( cot + 1 - cosec)

cot -1 + cosec)( cot+1 +cosec)/( cot+1- cosec)( cot +1 + cosec)

cot+ cosec)^2 - 1)/( cot +1)^2 - cosec^2)

cot^2 + cosec^2 + 2cotcosec -1)/( cot^2 + 1 + 2 cot - cosec^2)

As 1 + cot^2 = cosec^2

So

cot^2 + 1+ cot^2 + 2cot cosec -1)/( cosec^2 + 2cot - cosec^2)

2cot^2 + 2 cot cosec)/ 2cot

2 cot( cot + cosec)/ 2cot

cot + cosec