Math, asked by rishab9002, 1 year ago

prove:(cosA cotA)/1-sinA = 1+cosecA

Answers

Answered by manavjaison
18
Heya !!

Cos A  Cot A / 1 - Sin A 

Cos A * (Cos A /  Sin A) / 1 - Sin A                 {As Cot A = Cos A / Sin A}

Cos^2 A / Sin A / 1 - Sin A 

1 - Sin^2 A / Sin A (1 - Sin A)

(1 - Sin A)(1 + Sin A) / Sin A (1 - Sin A)          {As  a^2 - b^2 = (a - b)(a + b)}

By cancelling (1- Sin A) from numerator and denominator, we get,

1 + Sin A/ Sin A

By separating the denominator, we get,

1 / Sin A + Sin A / Sin A

1 / Sin A + 1 

Cosec A + 1                                                 {As 1 / Sin A = Cosec A}
 
or

1 + Cosec A = R.H.S.



Thanks !!
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