Home
Class 11
MATHS
In a Delta ABC, c cos^2 A/2+a cos^2C/2=(...

In a `Delta ABC, c cos^2 A/2+a cos^2C/2=(3b)/(2)` then show a,b,c are in A.P

Text Solution

Verified by Experts

Here , `C/2 (1+ cos A)+a/2(1+cos C )= 3b `
`rArr a+c+(c cos A+ a cos C)= 3b`
`rArr a+c+b = 3b `
`rArr a+c = 2b`
which shows a , b, c are in A.P
Promotional Banner

Topper's Solved these Questions

  • Solutions of Triangle & Binomial Theorem

    ALLEN|Exercise Illustration|27 Videos

  • Solutions of Triangle & Binomial Theorem

    ALLEN|Exercise EXERCISE-I|29 Videos

  • SOLUTION AND PROPERTIES OF TRIANGLE

    ALLEN|Exercise All Questions|62 Videos

  • TRIGNOMETRIC RATIOS AND IDENTITIES

    ALLEN|Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

In a Delta ABC, c cos ^(2)""(A)/(2) + a cos ^(2) ""(C ) /(2)=(3b)/(2), then a,b,c are in

If in a triangle ABC,b cos^(2)(A)/(2)+acos^(2)(B)/(2)=(3)/(2)c, then a,c,b are: quad in A.P.b.in G.P.c.in H.P.d.none of these

If in a triangle ABC,b cos^(2)((A)/(2))+a cos^(2)((B)/(2))=(3)/(2)c then a,c,b are:

If in a Delta ABCa cos^(2)((c)/(2))+c cos^(2)((A)/(2))=(3b)/(2) then the sides a,b and c

In Delta ABC,b(cos^(2)C)/(2)+c(cos^(2)B)/(2)=

If Delta ABC,quad if (cos A)/(2)=sqrt((b+c)/(2c)), then

In a Delta ABC, if sin^(2)A+cos^(2)C=cos^(2)B then sin B cos C+cos C sin A is equal to

If in a triangle ABC, b cos ^(2) "" A/2 + a cos ^(2) "" B/2 = (3c)/(2), then

If in a triangle ABC,a cos^(2)((C)/(2))ccos^(2)((A)/(2))=(3b)/(2), then the sides a,b, and c are in A.P.b.are in G.P.c. are in H.P.d.satisfy a+b=c.