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