Ifsin(x + y) = a + b, then the value of tan xis equal tosin(x

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If sin(x + y) = a + b , then the value of tan x is equal to
sin(x - y) a - b tan y

Here,

	sin(x + y)	=	a + b
	sin(x - y)		a - b

Using componendo and dividendo both sides we get,

	sin(x + y) + sin(x - y)
	sin(x + y) - sin(x - y)

=	a + b + a - b
	a + b - (a - b)

=	2a
	2a

∵ sinC + sinD

= 2sin		C + D		cos		C - D		sinC - sinD
		2				2

= 2cos		C + D		sin		C - D
		2				2

⇒	sinx.cosy	=	a
	siny.cosx		b

⇒	tan x	=	a
	tan y		b

If	sin(x + y)	=	a + b	, then the value of	tan x	is equal to
	sin(x - y)		a - b		tan y