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vizman

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hi,

can someone tell me how to do this.

Prove that sin ( A + B + C) cos (B + C) - cos ( A + B + C) sin (B + C) = sin A

thanks in advance
 

Riviet

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vizman said:
hi,

can someone tell me how to do this.

Prove that sin ( A + B + C) cos (B + C) - cos ( A + B + C) sin (B + C) = sin A

thanks in advance
Let S=sin, C=cos, A=a, B=b, C=c

LHS=C(b+c)[Sacos(b+c)+CaS(b+c)] - S(b+c)[CaC(b+c)-SaS(b+c)]

= SaC2(b+c) + CaS(b+c)C(b+c) - CaS(b+c)C(b+c) + SaS2(b+c)

= Sa[S2(b+c) + C2(b+c)]

=Sa(1)

=SinA

=RHS
:)

EDIT: :(
 
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vizman

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Riviet said:
Let S=sin, C=cos, A=a, B=b, C=c

LHS=C(b+c)[Sacos(b+c)+CaS(b+c)] - S(b+c)[CaC(b+c)-SaS(b+c)]

= SaC2(b+c) + CaS(b+c)C(b+c) - CaS(b+c)C(b+c) + SaS2(b+c)

= Sa[S2(b+c) + C2(b+c)]

=Sa(1)

=SinA

=RHS
:)

EDIT: :(

sorry how does that equal to 1.
 

vizman

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oh yeh. lol his substitution of sin for s confused me lol
 

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