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If n. sin(A+2B)=sinA, then prove that: t...

If n. `sin(A+2B)=sinA`, then prove that: `tan(A+B)=(1+n)/(1-n).tanB`

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`nsin(A+2B)=sinA`
`rArr n=(sinA)/(sin(A+2B))`
`therefore` RHS `=(1+n)/(1-n).tanB=(1+(sinA)/(sin(A+2B)))/(1-(sinA)/(sin(A+2B))).tanB`
`(sin(A+2B)+sinA)/(sin(A+2B)-sinA).tanB`
`=(2sinA(A+2B+A)/(2)cos(A+2B-A)/(2))/(2cos(A+2B+A)/(2)sin(A+2B-A)/(2)).tanB`
`=(sin(A+B)cosBsinB)/(cos(A+B)sinBcosB)`
`=tan(A+B)`=LHS Hence Proved.
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