Home
Class 12
MATHS
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

`a cos A = 2R sin A cos A = R sin 2A`
`rArr a cos A + b cos B + c cos C`
`=R (sin 2A + sin 2B + sin 2C)`
`= 4R sin A sin B sin C`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Concept application exercise 5.2|8 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Concept application exercise 5.3|3 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Illustration|86 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE )|8 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1119 Videos

Similar Questions

Explore conceptually related problems

(iii) a cosA + b cos B + c cos C = 4R sin A sin B sinC

In /_\ABC ,Prove that a cos A + b cos B + c cos C = 2a sin B sin C

If A+B+C=270^(@), then the value of cos 2A +cos 2B + cos 2C + 4 sin A sin B sin C is-

If cos A+ cos B + cos C=0 , prove that cos 3A + cos 3B + cos 3C = 12 cos A cos B cos C

If A,B,(A - B)are positive acute angles, then prove that geometrically : cos (A - B) = cos A cos B + sin A sin B

Prove that (b + c) cos A + (c + a) cos B + (a + b) cos C = 2s

Prove that sin2A + sin2B + sin2C = 4sinA · sinB · sin C

If sqrt2 cos A = cos B + cos^(3) B "and" sqrt2 sin A = sin B - sin^(3) B, "then the value of" sin (A - B) "will be"

If cos A = tan B , cos B= tan C, cos C= tanA , show that sin A= sin B= sin C= 2 sin 18^(@)

If A,B,C be the angles ofa triangle then prove that (sin A + sin B)(sin B + sin C)(sinC + sinA) gt sin A sin B sinC .