Question

prove that (cot x-cos x)/(cot x+cos x)=(cosec x-1)/(cosec x+1)​

Answer 1

Step-by-step explanation:

$we \: have \: to \: prove \: \\ \ \: \frac{ \cot(x) - \cos(x) }{ \cot(x ) + \cos(x) } = \frac{ cosec(x) - 1}{cosec(x) + 1} \\ on \: taking \: lhs \: \\ \\ \\ \frac{ \frac{ \cos(x) }{ \sin(x) } - \ \cos(x) }{ \frac{ \cos(x) }{ \sin(x) } + \cos(x) } \\ on \: taking \: common \frac{ \cos(x) }{ \sin(x) } \: in \: both \: numerator \: and \: denominator \\ it \: will \: cancel \: out \: and \: we \: get \: \\ \frac{1 - \sin(x) }{1 + \sin(x) } \\ we \: cn \: write \: sin(x) = \frac{1}{cosec(x)} \\ so \: we \: get \: \\ \frac{cosec(x) - 1}{cosec(x) + 1} = rhs \\ hence \:p roved$

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Answer 2

hííí fσllσw kαr dє nα чrrrrrrrrrr