Prove that a cos A + b cos B + c cos C =...

Prove that `a cos A + b cos B + c cos C = 4 R sin A sin B sin C`.

Text Solution

Verified by Experts

The correct Answer is:

`4 R sin A sinB sin C = R.H.S`.

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If A+B+C=(pi)/(2) , then prove that cos 2A + cos 2B + cos 2C=1+4 sin A sin B sin C .

If A+B+C=(3pi)/(2), prove that cos 2A+ cos 2B+ cos 2C=1-4 sin A sin B sin C .

Knowledge Check

Assertion (A): If A, B, C are the angles of a triangle such that cos A + cos B + Cos C = 0 = sin A + sin B + sin C then cos 3A + cos 3B + cos 3C = -3 Reason (R) : If cos alpha + cos beta + cos gamma = 0 = sin alpha + sin beta + singamma then cos 3 alpha + cos 3 beta + cos 3 gamma = 3 cos (gamma+alpha+beta)

A

Both A and R are true R is correct explanation to A

B

Both A and R are true but R is not correct explanation to A

C

A is true R is false

D

A is false R is true

If A+B+C=270^@ , " then " cos 2A + cos 2B+ cos 2C+ 4 sin A sin B sin C =

A

0

B

1

C

2

D

3

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If A+B+C=0 , then prove that sin 2A + sin 2B+ sin 2C=-4sin A sin B sin C .

Prove that (b-a) cos C + c (cos B- cos A) = c. sin ((A-B)/(2) ) cosec ((A+B)/(2))

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-PROPERTIES OF TRIANGLES-TEXTUAL EXERCISES ( EXERCISE - 10(a) ) II.

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