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If alpha+beta+gamma=2pi , then...

If `alpha+beta+gamma=2pi` , then

A

`tan (alpha)/(2)+tan (beta)/(2)+tan (gamma)/(2)=tan (alpha)/(2)tan (beta)/(2) tan (gamma)/(2)`

B

`tan (alpha)/(2)+tan (beta)/(2)+tan (beta)/(2)tan (gamma)/(2)+tan (gamma)/(2) tan (alpha)/(2)=1`

C

`tan (alpha)/(2)+tan (beta)/(2)+tan (gamma)/(2)=-tan (alpha)/(2) tan (beta)/(2)tan(gamma)/(2)`

D

`tan (alpha)/(2)+tan (beta)/(2)+tan (beta)/(2)tan (gamma)/(2) tan (gamma)/(2)tan(alpha)/(2)=0`

Text Solution

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The correct Answer is:
A
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MOTION-TRIGNOMETRIC RATIOS & IDENTITIES -Exercise 1
  1. Let alpha, beta be such that pi lt alpha lt beta lt 3pi, if sin alpha...

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  2. The value of tan 3A -tan 2A -tan A is equal to (A) tan 3A tan 2A tan A...

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  3. If alpha+beta+gamma=2pi , then

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  4. In a triangle ABC if tan A lt 0 then

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  5. If A+B=225^(@) then the value of (cotA)/(1+cotA).(cotB)/(1+cotB) is

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  6. The value of (sin 24^@ cos 6^@-sin 6^@sin 66^@)/(sin 21^@ cos 39^@-cos...

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  7. The valud of sin 12^(@) sin 48^(@) sin 54^(@) is equal to-

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  8. If A + B + C = (3pi)/2, then cos 2A + cos 2B + cos 2C is equal to (A) ...

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  9. The expression (cos 6x+6cos 4x+15 cos 2x+10)/(cos 5x+5 cos 3x+10 co...

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  10. The value of cos10^(@)-sin 10^(@) is

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  11. If 0 lt x lt pi and cos x + sin x = 1/2, then tan x is

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  12. If A lies in the third quadrant and 3 tan A-4 = 0, then 5 sin 2A + 3si...

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  13. For -pi/2 lt theta lt pi/2 ,(sin theta + sin 2 theta)/(1+cos theta + c...

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  14. Find the value of cos 12^(@)+cos 84^(@)+cos 156^(@)+cos 132^(@)

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  15. Prove that cos 36^(@) cos 72^(@) cos 108^(@) cos 144^(@)=1//16.

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  16. The value oif the expressin (1+cospi/10)(1+cos(3pi)/10)(1+cos(7pi)/10)...

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  17. (cos 20^(@)+8 sin 70^(@) sin 50^(@) sin 10^(@))/( sin^(2)80^(@)) is eq...

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  18. Which of the following is least ?

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  19. Find the value of x for which f(x)=sqrt(sinx-cosx) is defined, x in [0...

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  20. Find the number of solutions of sinx=x/(10)

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