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prove that 4sinalpha.sin(alpha+pi/3).sin...

prove that `4sinalpha.sin(alpha+pi/3).sin(alpha+(2pi)/3)=sin3alpha`

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CBSE COMPLEMENTARY MATERIAL-TRIGONOMETRIC FUNCTIONS -SHORT ANSWER TYPE QUESTIONS
  1. Draw the graph of cosx, sin x and tan x in [0, 2pi]

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  2. Draw sin x, sin 2x and sin 3x on same graph and with same scale

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  3. Evaluate(i) cos 36^(@) (ii)tan((13pi)/(12))

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  4. cos^4(pi/8)+cos^4((3pi)/8)+cos^4((5pi)/8)+cos^4((7pi)/8)=

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  5. If tanA=tanB=xa n dcotB-cotA=y , prove that cot(A-B)=1/x+1/y

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  6. If (sin(x+y))/(sin(x-y))=(a+b)/(a-b) , then show that (tanx)/(tany)=(...

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  7. if coxx=cosalpha.cosbeta then prove that tan((x+alpha)/2)*tan((x-alpha...

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  8. If tan(picostheta)=cot(pisintheta), then cos(theta-(pi)/(4))=pm(1)/(2s...

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  9. If sin(theta+alpha)=aa n dsin(theta+beta)=b , prove that cos2(alpha-be...

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  10. Find the range of 5 sin x – 12 cos x + 7

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  11. If alpha and beta are the solutions of the equation atan theta+ b s...

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  12. If alphaa n dbeta are the solutions of the equation at a ntheta+bs e c...

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  13. 2 sin^(2) beta + 4 cos( alpha+ beta) sin alpha sin beta + cos ( 2 alph...

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  14. If 81^(sin^2 x) + 81^(cos^2 x) = 30, where (pi//2) le x le pi, then x ...

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  15. Find the smallest positive number p for which the equation cos (p sin...

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  16. Find the smallest positive number p for which the equation cos (p sin...

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  17. Solve: 4sinxsin2xsin4x=sin3x

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  18. Solve: costheta cos2theta cos3theta =(1)/(4)

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  19. (1+ "cos "(pi)/(8)) (1+ "cos"(3pi)/(8)) (1+ "cos" (5pi)/(8)) (1+ "cos ...

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  20. prove that 4sinalpha.sin(alpha+pi/3).sin(alpha+(2pi)/3)=sin3alpha

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