If A, B , C are angles in a triangle, th...

If `A, B , C` are angles in a triangle, then the `sin ^(2)A+sin ^(2)B - sin ^(2) C =2 sin A sin B cos C`

A

`2 cos A sin B sin C `

B

`-2 cos A sin B sin C `

C

`2 sin A cos B sin C `

D

`2 sin A sin B cos C `

Text Solution

Verified by Experts

The correct Answer is:

D

Topper's Solved these Questions

TRIGONOMETRIC RATIOS AND IDENTITIES
DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 1 A ( TRIGONOMETRIC FUNCTIONS)|147 Videos
TRIGONOMETRIC RATIOS AND IDENTITIES
DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 1 B ( COMPOUNDS ANGLES )|106 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 are angles in a triangle, then prove that: sin^(2) A + sin^(2) B - sin^(2) C =2 sin A sin B cos C

If A, B , C are angles in a triangle, then prove that sin ^(2)A+ sin ^(2)B+sin^(2)C=2+2 cos A cos B cos C

If A, B, C are angles in a triangle , then prove that cos^(2)A+cos^(2)B-cos^(2)C=1-2sin Asin Bcos C.

If A, B, C are angles in a triangle , prove that sin A+ sin B -sin C =4sin. (A)/(2)sin. (B)/(2) cos. (C)/(2)

If A, B, C are angles of a triangle, then S. T sin 2A -sin 2B + sin 2C=4 CosA sin B CosC

If A , B , C are angles in a triangle , then prove that sin A + sin B + sin C =4 cos. (A)/(2) cos . (B)/(2) cos .(C)/(2)

If sin ^(2) A+ sin ^(2) B + sin ^(2) C then angle C =

b^(2) sin 2C + C^(2) sin 2B = 2 b sin A

If A, B, C are angles of a triangle , prove that sin 2A+sin 2B-sin 2C=4cos Acos B sin 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)

DIPTI PUBLICATION ( AP EAMET)-TRIGONOMETRIC RATIOS AND IDENTITIES -EXERCISE 2 ( SPEICAL TYPE QUESTIONS ) SET -4

If A, B , C are angles in a triangle, then the sin ^(2)A+sin ^(2)B - s...
Text Solution
|
A : sin theta + sin (pi+ theta ) + sin ( 2pi + theta ) ......... + si...
Text Solution
|
A : sqrt(1-sin^(2)100^@) sec 100^(@) =-1 R : sqrt(x^(2))=-x " if "...
Text Solution
|
A : sin^(2) 5^(@) + sin^(2) 10^(@) + ..... + sin^(2) 85^(@) =17//2 ...
Text Solution
|
A : If sin x + " cosec "x=2 , " then " sin^(n)x+"cosec"^(n)x=2 R : ...
Text Solution
|
A : cos 20^(@) + cos 100^(@) + cos 140^(@) =0 . R : cos theta + co...
Text Solution
|
A : sin 40^@ - sin 80^(@) + sin 160^(@) = 0 R : sin theta + sin(60^...
Text Solution
|
A : tan ( alpha - beta ) + tan ( beta - alpha ) + tan ( gamma - alpha...
Text Solution
|
A : If cos (x-y) =3 cos ( x+y) " then " cot x - cot y=2 R : If (a)/...
Text Solution
|
A : If cot A + cot B + cos C = sqrt(3) " then " Delta ABC is an equi...
Text Solution
|
A : cos 40^(@) cos 80^(@) cos 160^(@) =-1//8 R : cos theta cos (120...
Text Solution
|
A : cos 24^(@) cos 48^(@) cos 96^@ cos 168^(@) = 1//16 R : cos x ...
Text Solution
|
A : tan theta + 2 tan 2 theta + 4 tan 4 theta + 8 tan 8 theta - 16 co...
Text Solution
|
A : cos^(3) x + cos^(3)(120^@ + x) + cos^(3)(120^(@) - x)=(3)/(4) cos...
Text Solution
|
A : If x+y+z=xyz " then " sum(3x-x^(3))/(1-3x^(2))=Pi(3x-x^(3))/(1-3x^...
Text Solution
|
A : If x=sin(alpha - beta ) sin (gamma - delta), y=sin(beta - gamma ) ...
Text Solution
|
A : sum(r=1)^(n-1) cos^(2) (rpi)/(n)=(n)/(2)-1 R : cos alpha + cos...
Text Solution
|
Assertion (A) : "sin" (pi)/(n)+"sin" (3pi)/(n)+"sin"(5pi)/(n)+....+ to...
Text Solution
|
A : If A+B+C=180^(@) " then " cos^(2) A + cos^(2) B+ cos^2 C =1-2 cos ...
Text Solution
|
A : Period of sin8x+ cos 2x is pi R : Period of sin ax or cos ax "...
Text Solution
|
Assertion (A ) : The maximum value of 2 cos^(2) theta + sqrt(5) cos ...
Text Solution
|