Question

Hindi Pringle ABC if cos square A + cos square b + cos square equal to cos b into cos C + cos C into Cos A + Cos A into cos B​

Answer 1

Answer:

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If cos square A + cos square b + cos square C + 2 cos a × cos b × Cosc= 1 if a + b + C = 180 degree

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Answers : (1)

Solving RHS

2cosAcosBcosC =(2cosAcosB)cosC

=(cos(A+B) + cos(A-B))cosC

=cos(pi-C)cosC + cos(A-B)cos(pi-(A+B))

=-2cos^2C - 2cos(A+B)cos(A-B)

=-cos^2C - cos^2A + sin^2B

so,

1 - 2cosAcosBcosC = 1 + cos^2C + cos^2A - sin^2B

= 1 - sin^2B + cos^2C + cos^2A

= cos^2B + cos^2C + cos^2A

Answer 2

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Step-by-step explanation:

Let

I=cos

2

A+cos

2

B+cos

2

C−2cosAcosBcosC

1

(cos2A+1+cos2B+1+cos2C+1)−2cosAcosBcosC

(cos2A+cos2B+cos2C+3)−2cosAcosBcosC

Using

C=A+B

(2cos(A+B)cos(A−B)+cos2((A+B))+3)−2cosAcosBcosC

(2cos(A+B)cos(A−B)+2cos

2

(A+B)−1+3)−2cosAcosBcosC

(2cos(A+B)(cos(A−B)+cos(A+B))+2)−2cosAcosBcosC

Again using

A+B=C

1

(2cos(C)(2cosAcosB)+2)−2cosAcosBcosC

=2cosAcosBcosC+1−2cosAcosBcosC=1