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Prove that: (cosx-cosy)^2+(sinx-siny)^2=...

Prove that: `(cosx-cosy)^2+(sinx-siny)^2=4sin^2``(x-y)/2`

A

`4sin^(2)( (x-y)/(2))`

B

`4cos^(2)((x-y)/(2))`

C

`4sin((x+y)/(2))sin((x-y)/(2))`

D

`4cos((x+y)/(2))cos((x-y)/(2))`

Text Solution

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The correct Answer is:
A
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NAGEEN PRAKASHAN ENGLISH-TRIGNOMETRIC FUNCTIONS-EXERCISES 3P
  1. Maximum value of (3sintheta+4costheta) is:

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  2. If sinx+siny=sqrt(3)(cos y-cos x), then sin3x+sin3y= (a) ...

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  3. Prove that: (cosx-cosy)^2+(sinx-siny)^2=4sin^2(x-y)/2

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  4. If 2costheta=x+1/x, then 2cos2theta=?

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  5. If A+B=45^(@) , show that (1+tanA)(1+tan B)=2.

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  6. Prove that: cos^2pi/8+sin^2(3pi)/8+sin^2(5pi)/8sin^2(7pi)/8=2

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  7. If sinx+sin^(2)x=1 ,then cos^(4)x+cos^(2)x=?

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  8. If 4sin^(2)theta=3, then general value of theta is:

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  9. If sin7theta=cos5 theta, then general value of theta is:

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  10. If tan3theta=cottheta, then general value of theta is :

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  11. Find the general value of theta from the equation tantheta+tan2theta+t...

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  12. Solve the following equation : cottheta+t a ntheta=2

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  13. The solution of cos2theta=cos^(2)theta is:

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  14. cottheta=-sqrt(3) and cosec theta=2

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  15. Solve: 2sin^(2)theta+sin^(2)2theta=2

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  16. If sqrt(3)sintheta-costheta=0, then one general value of theta is:

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  17. In DeltaABC, a=12 m, angleB=30^(@) and angleC=90^(@), then area of Del...

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  18. In DeltaABC, a=12 cm, angleB=30^(@) and angleC=90^(@), then area of De...

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  19. In DeltaABC, cotA/2, cotB/2, cotC/2 are in A.P., then the true stateme...

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  20. In DeltaABC, if a,b,c are in A.P. prove that: cot(A/2),cot(B/2), cot...

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