In any ABC- prove that- cos Aa-cos Bb-cos Cc-a2-b2-c22abc-

cosAa + cosBb + cosCc =b^2+c^2 a^22bc × a+c^2 + a^2 b^22ca × b + a^2 + b^2 c^22ab × c #160; #160;(Using cosine rule) =b^2 + c^2 a^2 + ...

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Byju's Answer

Standard XII

Mathematics

General Solution of Trigonometric Equation

In any ABC,...

Question

In any $△ A B C$ , prove that: $\frac{cos A}{a} + \frac{cos B}{b} + \frac{cos C}{c} = \frac{a^{2} + b^{2} + c^{2}}{2 a b c}$ .

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Solution

$\frac{c o s A}{a} + \frac{c o s B}{b} + \frac{c o s C}{c}$
$= \frac{b^{2} + c^{2} - a^{2}}{2 b c \times a} + \frac{c^{2} + a^{2} - b^{2}}{2 c a \times b} + \frac{a^{2} + b^{2} - c^{2}}{2 a b \times c}$ (Using cosine rule)

$= \frac{b^{2} + c^{2} - a^{2} + c^{2} + a^{2} - b^{2} + a^{2} + b^{2} - c^{2}}{2 a b c} = \frac{a^{2} + b^{2} + c^{2}}{2 a b c}$

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Similar questions

Q. In a

△ A B C

, prove that

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

Q. Show that

\frac{cos A}{a} + \frac{cos B}{b} + \frac{cos C}{c} = \frac{a^{2} + b^{2} + c^{2}}{2 a b c}

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 :-

\frac{cos A}{(c cos B + b cos C)} + \frac{cos B}{(a cos C + cos A)} + \frac{cos C}{(a cos B + b cos A)} = \frac{a^{2} + b^{2} + c}{2 a b c}

Q. Prove that:

\frac{a^{2} - b^{2}}{cos A + cos B} + \frac{b^{2} - c^{2}}{cos B + cos C} + \frac{c^{2} - a^{2}}{cos C + cos A} = 0

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In any △ABC, prove that: cosAa+cosBb+cosCc=a2+b2+c22abc.

cosAa+cosBb+cosCc=b2+c2−a22bc×a+c2+a2−b22ca×b+a2+b2−c22ab×c (Using cosine rule)=b2+c2−a2+c2+a2−b2+a2+b2−c22abc=a2+b2+c22abc

In any $△ A B C$ , prove that: $\frac{cos A}{a} + \frac{cos B}{b} + \frac{cos C}{c} = \frac{a^{2} + b^{2} + c^{2}}{2 a b c}$ .