Which of the following is true in a tria...

Which of the following is true in a triangle `ABC?` (1) `(b+c) sin((B_C)/2)=2a cos(A/2)` (2) `(b+c)cos(A/2)= 2a sin((B-C)/2)`

`(b+c)sin.(B-C)/(2)=2acos.(A)/(2)`

`(b+c)cos.(A)/(2)=2asin.(B-C)/(2)`

`(b-c)cos.(A)/(2)=asin.(B-C)/(2)`

`(b-c)sin.(B-C)/(2)=2acos.(A)/(2)`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

TRIGONOMETRIC FUNCTIONS
TARGET PUBLICATION|Exercise Competitive Thinking|218 Videos
TRIGONOMETRIC FUNCTIONS
TARGET PUBLICATION|Exercise Evaluation Test|34 Videos
TRIGONOMETRIC FUNCTIONS
TARGET PUBLICATION|Exercise Evaluation Test|34 Videos
THREE DIMENSIONAL GEOMETRY
TARGET PUBLICATION|Exercise Evaluation Test|9 Videos
VECTORS
TARGET PUBLICATION|Exercise Evaluation Test|18 Videos

Similar Questions

Explore conceptually related problems

Which of the following is true in a triangle ABC?(1)(b+c)sin((B_(C))/(2))=2a cos((A)/(2))(2+c)cos((A)/(2))=2a sin((B-C)/(2))

Show that, in a triangle ABC. a^(2) = (b - c)^(2) cos^(2) (A/2) + (b + c)^(2) sin^(2) (A/2) .

In triangle ABC,a,b,c are the lengths of its sides and A,B,C are the angles of triangle ABC .The correct relation is given by (a) (b-c)sin((B-C)/(2))=a(cos A)/(2) (b) (b-c)cos((A)/(2))=as in(B-C)/(2)(c)(b+c)sin((B+C)/(2))=a(cos A)/(2)(d)(b-c)cos((A)/(2))=2a(sin(B+C))/(2)

In any triangle ABC, (a+b)^2 sin^2 ((C )/(2))+(a-b)^2 cos^2 ((C )/(2))= .

In any triangle ABC,show that: 2a cos((B)/(2))cos((C)/(2))=(a+b+c)sin((A)/(2))

In any triangle ABC, prove that (i) (a-b)/( c)=("sin"(A-B)/(2))/("cos"( C)/(2)) (ii) (b-c)/(a)=("sin"(B-C)/(2))/("cos"(A)/(2))

Prove in any triangle ABC that (i) a(cos B+cos C)=2(b+c) "sin"^(2)(A)/(2) (ii) a(cos C- cosB)= 2(b-c )"cos"^(2)(A)/(2)

In any triangle ABC, prove that following: sin((B-C)/(2))=(b-c)/(a)(cos A)/(2)

If A, B, C are angle of a triangle ABC, then the value of the determinant |(sin (A/2), sin (B/2), sin (C/2)), (sin(A+B+C), sin(B/2), cos(A/2)), (cos((A+B+C)/2), tan(A+B+C), sin (C/2))| is less than or equal to

TARGET PUBLICATION-TRIGONOMETRIC FUNCTIONS -Critical Thinking

In a triangle ABC, if a = 2, B=60^(@)andC=75^(@), then b =
Text Solution
|
If the angles of a triangle are in the ratio 2 : 3 : 7 ,then the sides...
Text Solution
|
Which of the following is true in a triangle ABC? (1) (b+c) sin((BC...
Text Solution
|
Prove that (1+cos(A-B)cosC)/(1+cos(A-C)cosB)=(a^(2)+b^(2))/(a^(2)+c^(2...
Text Solution
|
In DeltaABC,(cos.(1)/(2)(B-C))/(sin.(1)/(2)A)=
Text Solution
|
If the sides of a triangle are 6 cm, 10 cm and 14 cm, then what is the...
Text Solution
|
If the angles A, B, and C of a triangle ABC are in AP and the sides a,...
Text Solution
|
If the angles of a triangle ABC are in A.P., then
Text Solution
|
In DeltaABC,(cosA)/(a)+(cosB)/(b)+(cosC)/(c)=
Text Solution
|
The ratio of the sides of a triangle ABC is 1: sqrt3: 2. The ratio A: ...
Text Solution
|
In DeltaABC,(a-b)^(2)cos^(2).(C)/(2)+(a+b)^(2)sin^(2).(C)/(2)=
Text Solution
|
If in triangle ABC, cosA=(sinB)/(2sinC), then the triangle is
Text Solution
|
The sides of a triangle are sin alpha, cos alpha and sqrt(1+ sin alpha...
Text Solution
|
In DeltaABC,1-tan.(A)/(2)tan.(B)/(2)=
Text Solution
|
In DeltaABC,"if "2s=a+b+c, then the value of (s(s-a))/(bc)-((s-b)(s-c)...
Text Solution
|
If in a triangle A B C ,acos^2(C/2)ccos^2(A/2)=(3b)/2, then the sides ...
Text Solution
|
If in a triangle ABC, (s-a)(s-b)= s(s-c), then angle C is equal to
Text Solution
|
In any DeltaABC,("tan"(A)/(2)-"tan"(B)/(2))/("tan"(A)/(2)+"tan"(B)/(2)...
Text Solution
|
In !ABC , if sin^(2)A/2,sin^(2)B/2,sin^(2)C/2 be in H.P., then a , b ,...
Text Solution
|
If in a triangleABC , a = 6, b=3 and cos(A-B)=4/5 then find its area...
Text Solution
|