Question

prove that 1/1-cosA + 1/1+cos A = 2 cosec× cosec A

Answer 1

Heya mate, Here is ur answer

$\frac{1}{1 - cos \: a} + \frac{1}{1 + cos \: a}$


Taking LCM


$\frac{1 + cos \: a + 1 - cosa}{(1 - cos \: a)(1 + cos \:) }$

Using identity (a-b)(a+b)=a^2 -b^2

$\frac{2}{1 {}^{2} - cos {}^{2} \: a }$

$\frac{2}{1 - cos {}^{2} \: a }$


Now, we know,

sin^2 A+ cos ^2 A=1

sin^2 A=1-cos^2 A

So ,

$= \frac{2}{sin {}^{2} a}$


$= 2 \times \frac{1}{sin \: a} \times \frac{1}{sin \: a}$


We know that 1/Sin A = cosec A

$= 2 \times cosec \: a \: \times cosec \: a$


$= 2 {cosec}^{2} a$


Hence proved

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@Laughterqueen

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