Question

If 2sinx/1+Cosx+sinx =p then 1-cosx +sinx/1+sinx

Answer 1

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Answer 2

Answer:

$1+sinx-cosx=p(sinx+1)$

Step-by-step explanation:

$Given\:\frac{2sinx}{1+cosx+sinx}=p$

$\implies \frac{2sinx(1+sinx-cosx)}{(1+sinx+cosx)(1+sinx-cosx)}=p$

$\implies \frac{2sinx(1+sinx-cosx)}{(1+sinx)^{2}-cos^{2}x)}=p$

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

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

$\implies \frac{2sinx(1+sinx-cosx)}{sin^{2}x+2sinx+sin^{2}x}=p$

$\implies \frac{2sinx(1+sinx-cosx)}{2sin^{2}x+2sinx}=p$

$\implies \frac{2sinx(1+sinx-cosx)}{2sinx(sinx+1)}=p$

$\implies \frac{1+sinx-cosx}{sinx+1}=p$

$\implies 1+sinx-cosx=p(sinx+1)$

Therefore,

$1+sinx-cosx=p(sinx+1)$

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