Question

This question is of trigonometry so please answer step by step with pic/attachment

Answer 1

Answer:

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Answer 2

Question :-

Prove that

$\frac{1 + \cos(x) }{ \sin {}^{2} (x ) } = \frac{1}{1 - \cos(x) }$

Solution :-

$\frac{1 + \cos(x) }{ \sin {}^{2} (x) } = \frac{1}{1 - \cos(x) }$

Now do cross Multiplication

$(1 + \cos(x ))(1 - \cos(x) ) = \sin {}^{2} (x) \\ \\ 1 - \cos {}^{2} (x) = \sin {}^{2} (x)$

As,

$1 - \cos {}^{2} (x) = \sin {}^{2} (x)$

Hence,

$\sin {}^{2} (x) = \sin {}^{2} (x)$

LHS =RHS - - - (PROVED)