In a triangle ABC, if a, b, c are the sides opposite to angle A,B, C respectively, then value of |b cos C&a&c cos B c cos A&b&a cos C a cos B&c&b cos A| is

Question

In a triangle ABC, if a, b, c are the sides opposite to angle A,B, C respectively, then value of |b cos C&a&c cos B c cos A&b&a cos C a cos B&c&b cos A| is (A) 1 (B) -1 (C) 0 (D) a cos A+b cos B+c cos C

Tardigrade Admin · Accepted Answer

Q. In a triangle ABC, if a, b, c are the sides opposite to angle
A,B, C respectively, then value of $∣ ∣ b cos C c cos A a cos B a b c c cos B a cos C b cos A ∣ ∣$ is

1

-1

0

$a cos A + b cos B + c cos C$

$∣ ∣ b cos C c cos A a cos B a b c c cos B a cos C b cos A ∣ ∣$
Apply $C_{1} \to C_{1} + C_{3}$ and using projection rule,
$D = ∣ ∣ b cos C c cos A a cos B a b c c cos B + b cos C a cos C + c cos A b cos A + a cos B ∣ ∣$
$= ∣ ∣ b cos C c cos A a cos B a b c a b c ∣ ∣ = 0$

Q. In a triangle ABC, if a, b, c are the sides opposite to angle A,B, C respectively, then value of ∣∣​bcosCccosAacosB​abc​ccosBacosCbcosA​∣∣​ is

1

-1

0

acosA+bcosB+ccosC

∣∣​bcosCccosAacosB​abc​ccosBacosCbcosA​∣∣​ Apply C1​→C1​+C3​ and using projection rule, D=∣∣​bcosCccosAacosB​abc​ccosB+bcosCacosC+ccosAbcosA+acosB​∣∣​ =∣∣​bcosCccosAacosB​abc​abc​∣∣​=0

Q. In a triangle ABC, if a, b, c are the sides opposite to angle
A,B, C respectively, then value of $∣ ∣ b cos C c cos A a cos B a b c c cos B a cos C b cos A ∣ ∣$ is

$a cos A + b cos B + c cos C$

$∣ ∣ b cos C c cos A a cos B a b c c cos B a cos C b cos A ∣ ∣$
Apply $C_{1} \to C_{1} + C_{3}$ and using projection rule,
$D = ∣ ∣ b cos C c cos A a cos B a b c c cos B + b cos C a cos C + c cos A b cos A + a cos B ∣ ∣$
$= ∣ ∣ b cos C c cos A a cos B a b c a b c ∣ ∣ = 0$