Prove that cos C-cos A-c-a-cos B-b-1-b

L.H.S =cos C+cos A/c+a+cos B/b =bcos C+bcos A+(c+a)cos B/b(c+a) =(bcos C+ccos B)+(bcos A+acos B)/b(c+a) =a+c/b(c+a)=1/b = R.H.S. Hence prov ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Summation by Sigma Method

Prove that ...

Question

Prove that $\frac{cos C + cos A}{c + a} + \frac{cos B}{b} = \frac{1}{b}$

Open in App

Solution

L.H.S $= \frac{cos C + cos A}{c + a} + \frac{cos B}{b}$

$= \frac{b cos C + b cos A + (c + a) cos B}{b (c + a)}$
$= \frac{(b cos C + c cos B) + (b cos A + a cos B)}{b (c + a)}$
$= \frac{a + c}{b (c + a)} = \frac{1}{b} =$ R.H.S. Hence proved.

Suggest Corrections

Similar questions

Q. Prove that

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

Q. Prove that

cos A + cos B + cos C = 1 + r / R

Q. If A, B, C be the angles of a triangle, then prove that

∣ ∣ ∣ ∣ \begin{matrix} - 1 & c o s C & c o s B c o s C & - 1 & c o s A c o s B & c o s A & - 1 \end{matrix} ∣ ∣ ∣ ∣

= 0

If A+B+C = $π$ , prove that cos A + cos B - cos C = $(4 cos \frac{A}{2} cos \frac{B}{2} sin \frac{C}{2}) - 1$

Q. If

\frac{b + c}{11} = \frac{c + a}{12} = \frac{a + b}{13},

prove that

\frac{cos A}{7} = \frac{cos B}{19} = \frac{cos C}{25}

Join BYJU'S Learning Program

Prove that cosC+cosAc+a+cosBb=1b

L.H.S =cosC+cosAc+a+cosBb=bcosC+bcosA+(c+a)cosBb(c+a)=(bcosC+ccosB)+(bcosA+acosB)b(c+a)=a+cb(c+a)=1b= R.H.S. Hence proved.

Prove that $\frac{cos C + cos A}{c + a} + \frac{cos B}{b} = \frac{1}{b}$

L.H.S $= \frac{cos C + cos A}{c + a} + \frac{cos B}{b}$

$= \frac{b cos C + b cos A + (c + a) cos B}{b (c + a)}$
$= \frac{(b cos C + c cos B) + (b cos A + a cos B)}{b (c + a)}$
$= \frac{a + c}{b (c + a)} = \frac{1}{b} =$ R.H.S. Hence proved.