If A+B+ C =pi, then prove that cos ^(2) ...

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

A

`2 cos""(A)/(2) cos""(B)/2""sin""(C)/(2)`

B

`2 cos""(A)/2 sin""(B)/(2) cos""(C)/2`

C

`2+2 cos""(A)/(2) cos""(B)/(2)cos""(C)/2`

D

`2+2sin""(A)/(2) sin""(B)/(2) sin""(C)/(2)`

Text Solution

Verified by Experts

The correct Answer is:

D

Promotional Banner

Promotional Banner

Topper's Solved these Questions

TRIGONOMETRIC RATIOS AND IDENTITIES
DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 1 F ( PERIODIC FUNCTIONS )|39 Videos
TRIGONOMETRIC RATIOS AND IDENTITIES
DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 1 G ( VARIATION IN TRIGONOMETRIC FUNCTIONS )|67 Videos
TRIGONOMETRIC RATIOS AND IDENTITIES
DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 1 D ( TRANSFORMATIONS )|94 Videos
TRIGONOMETRIC EQUATIONS
DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 (SPECIAL TYPE QUESTIONS) SET - 4|4 Videos

Similar Questions

Explore conceptually related problems

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

If A+B+C=0 , then prove that cos ^(2)A+ cos ^(2) B + cos ^(2) C =1+2 cos A cos B cos C

If A, B , C are angles of a triangle, then P. T sin ^(2) . (A)/(2)+ sin^(2). (B)/(2) - sin ^(2). (C)/(2) =1-2 cos. (A)/(2) cos. (B)/(2) sin .(C)/(2)

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

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

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= 2S , then prove that (i) sin (S-A)+sin (S-B) + sin C=4 cos . (S-A)/(2) cos. (S-B)/(2) sin .(C)/(2) (ii) cos (S-A)+cos (S-B)+cos C=-1+4 cos. (S-A)/(2) cos.(S-B)/(2)cos. (C)/(2)

( b- c)^(2) cos ^(2) ( A//2) + ( b+ c) ^(2) sin ^(2) ( A//2) =

( a- b) ^(2) cos ^(2) ""(C ) /(2) + ( a+b) ^(2) sin ^(2) "" ( C )/(2) =

If A+B+C=180^(@) then prove that cos^(2)A+cos^(2)B+cos^(2)C=1-2cosAcosBcosC

DIPTI PUBLICATION ( AP EAMET)-TRIGONOMETRIC RATIOS AND IDENTITIES -EXERCISE 1 E ( TRIGONOMETRIC IDENTITIES )

If A+B+C=180^(@) " then " sin^(2)""(A)/(2)+sin^(2)""(B)/2+sin^(2)""(C)...
Text Solution
|
If A+B+C=180^@ " then " sin^(2)""(A)/(2)-sin^(2)""(B)/(2)+sin^(2)""(C)...
Text Solution
|
If A+B+ C =pi, then prove that cos ^(2) (A/2)+ cos ^(2) (B/2) +cos ^(2...
Text Solution
|
In Delta ABC, cos^(2)""(A)/(2)+cos^(2)""(B)/(2)-cos^(2)""(C)/2=
Text Solution
|
If A+B+C=180^(@) then prove the following: "cos"A/2+"cos"B/2+"cos"C/...
Text Solution
|
If A, B, C are the angles in a triangle then prove that sin .(A)/(2)+...
Text Solution
|
If A+B+C=180^@ " then " sin 3A+ sin 3B+ sin 3C=
Text Solution
|
If A+B+C=180^(@) " then " cos 3A + cos 3B+ cos 3C=
Text Solution
|
If A+B+C=180^@ then sin^(3) A cos (B-C) + sin^(3)B cos(C-A)+ sin^(3) ...
Text Solution
|
If A+B+C=180^(@) " then " tan^(2) ""(A)/(2) + tan^(2)""(B)/(2) + tan^(...
Text Solution
|
In Delta ABC , sum sin""(A)/(2) cos""((B-C)/(2))=
Text Solution
|
In Delta ABC, if tan ""(A)/(2), tan""(B)/(2) , tan""(C)/(2) are in A.P...
Text Solution
|
If A+B+C=pi and cos A = cos B cos C " then " cot B cot C =
Text Solution
|
If A+B+C= 90^(@) " then " sin 2A+ sin 2B- sin 2C=
Text Solution
|
If A+ B+C= 180^(@) " then " cos 2A+ cos 2B + cos 2C+ 1=
Text Solution
|
If A+B+C=(pi)/(2), then prove that sin ^(2) A+ sin ^(2) B + sin ^(2) C...
Text Solution
|
If A+B+C=90^(@) " then " cos^(2) A + cos^(2) B + cos^(2) C =
Text Solution
|
If A+B+C=90^(@) " then " ( cos 2A + cos 2 B+ cos 2C-1)/( sin A sin B s...
Text Solution
|
If A+B+C=0, then prove that sin 2A + sin 2B+ sin 2C=-4sin A sin B sin ...
Text Solution
|
If A+B+C=0^@ " then " sin A + sin B + sin C =
Text Solution
|