Question 19594
{{{(1+ sin x +cos x)^2=2(1+ sin x)(1+ cos x)}}}
Left hand side:
1 + (sin^2)x + (cos^2)x + 2(1*sinx+sinx*cosx+1*cosx)
we know that (sin^2)x + (cos^2)x = 1
{{{1+1+2(sinx+cosx+sinx*cosx)}}}
{{{2+2sinx+2cosx+2sinx*cosx}}}
{{{2(sinx+cosx+sinx*cosx)}}}
{{{2(cosx+sinx+sinx*cosx)}}}
{{{2(cosx+sinx(1+cosx))}}}
{{{2(1+sinx)(1+cosx)}}}
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which is equal to the right hand side
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Hope this helps,
Prabhat