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(sinx+sin3x)/(cosx+cos3x) = tan2x...

`(sinx+sin3x)/(cosx+cos3x) = tan2x`

Text Solution

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LHS `=(sinx+sin3x)/(cosx+cos3x)`
`=(2sin(x+3x)/(2)cos(x-3x)/(2))/(2cos(x+3x)/(2)cos(x-3x)/(2)) = (sin(x+3x)/(2))/(cos(x+3x)/(2))`
`=(sin2x)/(cos2x)=tan2x`=RHS Hence Proved.
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