In ABC-prove that c cos A- -a cos C- -bcos-

c cos (A α )+a cos (C+α )=bcosα Consider, nbsp; c cos (A α )+a cos (C+α ) =ccos Acosα+csin Asinα +acos Ccosα asin Csinα =cosα (acos C+ccos ...

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Standard XII

Mathematics

Circular Measurement of Angle

In ABC,prov...

Question

In $△ A B C$ ,prove that $c cos (A - α) + a cos (C + α) = b cos α$

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Solution

$c cos (A - α) + a cos (C + α) = b cos α$
Consider, $c cos (A - α) + a cos (C + α)$
$= c cos A cos α + c sin A sin α + a cos C cos α - a sin C sin α$
$= cos α (a cos C + c cos A) + sin α (c sin A - a sin C)$
$= b cos α + sin α (0)$ ( $\frac{a}{sin A} = \frac{c}{sin C}$ )
$= b cos α$

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Similar questions

Q. In ∆ABC, prove that if θ be any angle, then b cosθ = c cos (A − θ) + a cos (C + θ).

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$\frac{c o s A}{c c o s B + b c o s C} + \frac{c o s B}{a c o s C + c c o s A} + \frac{c o s C}{a c o s B + b c o s A} = \frac{a^{2} + b^{2} + c^{2}}{2 a b c}$

Q. If a

tan α + b tan β = (a + b) tan (\frac{α + β}{2})

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In $Δ A B C, c c o s (A - α) + α c o s (C + α) =$

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In △ABC,prove that ccos(A−α)+acos(C+α)=bcosα

ccos(A−α)+acos(C+α)=bcosαConsider, ccos(A−α)+acos(C+α)=ccosAcosα+csinAsinα+acosCcosα−asinCsinα=cosα(acosC+ccosA)+sinα(csinA−asinC)=bcosα+sinα(0) (asinA=csinC)=bcosα

In $△ A B C$ ,prove that $c cos (A - α) + a cos (C + α) = b cos α$

$c cos (A - α) + a cos (C + α) = b cos α$
Consider, $c cos (A - α) + a cos (C + α)$
$= c cos A cos α + c sin A sin α + a cos C cos α - a sin C sin α$
$= cos α (a cos C + c cos A) + sin α (c sin A - a sin C)$
$= b cos α + sin α (0)$ ( $\frac{a}{sin A} = \frac{c}{sin C}$ )
$= b cos α$