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If sinA + sinB = a and cosA+cosB=b, prov...

If `sinA + sinB = a` and `cosA+cosB=b`, prove that:
i) `sin(A+B)=(2ab)/(a^(2)+b^(2))`
ii) `tan(A+B)= (2ab)/(b^(2)-a^(2))`

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NAGEEN PRAKASHAN ENGLISH-TRIGNOMETRIC FUNCTIONS-EXERCISES 3D
  1. Prove that: cos^2A+cos^2B-2cosA\ cos B cos\ (A+B)=sin^2(A+B)

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  2. If tan B=(n sin A cos A)/(1-n cos^(2)A), then tan(A+B) equals to

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  3. If tan B=(n sin A cos A)/(1-n cos^(2)A), then tan(A+B) equals to

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  4. If 2tanB +cotB=tanA, prove that: 2tan(A-B)=cotB

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  5. i) If tan (A+B) = n tan (A-B), prove that: (n+1)/(n-1) = (sin2A)/(sin...

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  6. If A+B=225^(@), then find the value of (cotA)/(1+cotA)xx(cot B)/(1+cot...

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  7. If cos(A+B)sin(C-D)="cos"(A-B)"sin"(C+D) , then write the value of t a...

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  8. If alphaa n dbeta are the solutions of acostheta+bs intheta=c , then s...

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  9. If sinA + sinB = a and cosA+cosB=b, prove that: i) sin(A+B)=(2ab)/(a...

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  10. Prove that the value of 5 costheta+3 cos(theta+pi/3) lies between -7 a...

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  11. Prove that: tan10^(@)tan50^(@)+tan50^(@)tan70^(@)+tan70^(@)tan170^(@...

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  12. prove that sin2x+2sin4x+sin6x=4cos^(2)x.sinx

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  13. Prove that: (sin7A+sin5A+sin9A+sin3A)/(cos3A+cos5A+cos7A+cos9A)= tan...

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  14. Prove that sinA+sin2A+sin4A+sin5A=4 cos(A/2)cos((3A)/2)sin3A

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  15. Prove that: ("cos"8Acos5A-cos12 Acos9A)/("sin"8Acos5A+cos12 Asin9A)=ta...

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  16. If cosA=kcos(A-2B), prove that: tan(A-B)tanB= (1-k)/(1+k)

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  17. If cos e cA+secA=cos e c B+s e cB , prove that: "tanAtanB"=cot(A+B)/2

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  18. i) If sinA+sinB=sqrt(3)(cosB-cosA), prove that: sin3A+sin3B=0 ii) If...

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  19. Show that : cos A+ cosB + cosC+ cos(A+B+C) = 4cos""(B+C)/(2)cos""(C+A)...

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  20. If (sin(theta+alpha))/(cos(theta-alpha))=(1-m)/(1+m) , prove that tan(...

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