Question

prove that Sin ( A + B ) = Sin A Cos B + Cos A SinB

Answer 1

In ∆ ABF

Sin ( A + B ) = BF/AF

= BE/AF + EF/AF

= CD /AF + EF / AF

Sin (A + B) => (CD/AD * AD/AF) + (EF/FD * FD/AF) ..,...(I)


In ∆ ACD CD/AD = Sin A ,

in ∆ADF AD/AF = Cos B,

in ∆FED EF/FD = Cos A,

in ∆ADF FD/AF = Sin B,

putting these values in (I) we get

Sin (A + B) = SinACosB + CosASinA

PROVED
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❤BE BRAINLY ❤

Answer 2

Answer:In ∆ ABF

Sin ( A + B ) = BF/AF

= BE/AF + EF/AF

= CD /AF + EF / AF

Sin (A + B) => (CD/AD * AD/AF) + (EF/FD * FD/AF) ..,...(I)

In ∆ ACD CD/AD = Sin A ,

in ∆ADF AD/AF = Cos B,

in ∆FED EF/FD = Cos A,

in ∆ADF FD/AF = Sin B,

putting these values in (I) we get

Sin (A + B) = SinACosB + CosASinA

PROVED