Question #7b2a4

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Answer 1 · 2016-11-27T15:16:40

$(\frac{cot x}{1 + csc x}) + sin x csc x$ $(cotx /(1+csc x)) + sinx cscx$

$cot x = \frac{1}{tan x} = \frac{cos x}{sin x}$ $cotx=1/tanx=cosx/sinx$

$1 + csc x = 1 + \frac{1}{sin x} = \frac{sin x + 1}{sin x}$ $1+cscx=1+1/sinx=(sinx+1)/sinx$

$csc x = \frac{1}{sin x}$ $cscx=1/sinx$

$sinxcscx=cancel(sinx)1/cancel(sinx)=1$

$(cotx /(1+csc x)) + sinx cscx=$

$(cosx/sinx)/((sinx+1)/sinx)+1=$

$cosx/cancel(sinx) xx(cancel(sinx)(1))/(sinx+1)+1=$

$cosx/(sinx+1)+1=$

$(cosx+sinx+1)/(sinx+1)=$

$1+cosx/(sinx+1)$