Question

1/1+cos + 1/1-cos=2/sin² prove it.​

Answer 1

★verifie:-

$\implies \: \frac{1}{1 + \cos \theta} + \frac{1}{1 - \cos \theta } = \frac{2}{ \sin {}^{2} \theta }$

★solution:-

$\pink{lhs}$

$\implies \: \frac{1}{1 + \cos \theta } + \frac{1}{1 - \cos \theta} \\ \\ \implies \: \frac{1 - \cos \theta + 1 + \cos \theta }{(1 + \cos \theta)(1 - \cos \theta) }$

we know that formula of

$\implies \star \pink{(a + b)(a - b) = a {}^{2} - b {}^{2} }$

$\implies \: \frac{2}{1 - \cos {}^{2} \theta }$

we know that

$\implies \star \pink{1 - \cos {}^{2} \theta = \sin {}^{2} \theta }$

$\implies \: \frac{2}{ \sin {}^{2} \theta } \: \: \: \: \: \: \: \: \: \: \red{(hence \: proved \: )}$

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I hope it helps you