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prove sin alpha+sin(alpha+(2pi)/3)+sin (...

prove `sin alpha+sin(alpha+(2pi)/3)+sin (alpha+(4pi)/3)=0`

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Prove that sinalpha+sin(alpha+(2pi)/3)+sin(alpha+(4pi)/3)=0 .

Prove that tan (alpha+ (pi)/(3)) tan (alpha-(pi)/(3))+ tan alpha tan (alpha+(pi)/(3)) +tan (alpha-(pi)/(3)) tan alpha+3=0

sin3alpha = 4 sin alpha sin(x+alpha)sin(x-alpha)

If alpha=(2pi)/(7) then prove that sin alpha sin 2 sin 4 alpha =-(sqrt(7))/(8)

If alpha=(pi)/(8 n) then prove that sin^(2) alpha+ sin^(2)3 alpha+ sin ^(2) 5 alpha+.. to 2n terms =n.

If cos3theta=cos3alpha, then the value of sintheta can be given by +-sinalpha (b) sin(pi/3+-alpha) sin((2pi)/3+alpha) (d) sin((2pi)/3-alpha)

Prove the following identities: (sin alpha sin 11 alpha + sin 3 alpha sin 7 alpha)/(sin alpha cos 11 alpha + sin 3 alpha cos 7 alpha)= tan 8 alpha

Prove that, (sin alpha + cos alpha)/(cos alpha-sin alpha)=tan2 alpha + sec 2 alpha

Find the general solution of the equation sin 3 alpha = 4 sin alpha sin(x + alpha) sin(x - alpha) , given sin alpha ne 0 .

If alpha= (2pi)/(7) , then prove that cos alpha+ cos 2 alpha+ cos 4alpha=-(1)/(2) . Hence, deduce that sin alpha+ sin 2alpha+ sin 4alpha=(sqrt(7))/(2)

PATHFINDER-TRIGONOMETRIC RATIOS AND IDENTITIES-QUESTION BANK
  1. Evaluate : cos12^@cos24^@cos36^@cos48^@cos72^@cos84^@

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  2. If alpha,beta,gamma are in A.P. show that cot beta=(sin alpha-sin gamm...

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  3. prove sin alpha+sin(alpha+(2pi)/3)+sin (alpha+(4pi)/3)=0

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  4. Prove that (cos 7x+cos 5x)/(sin7x-sin 5x)=cotx

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  5. if tan( (pi)/9),x, tan ((5pi)/18) are in A.P. and tan(pi/9), y,tan ((7...

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  6. find the value of k which satisfy tan theta +tan(theta+pi/3)+tan (thet...

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  7. sin^3x.sin3x=underset(mrarr0)(oversetnsumCmcosmx is an identity in x,w...

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  8. Find sin( (pi)/n)+sin ((3pi)/n)+sin ((5pi)/n)+……..to n terms

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  9. Find theta if sin theta -cos theta lt0

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  10. Find A/2 if 2sin (A/2)=sqrt(1+sin A)+sqrt(1-sin A)

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  11. Find the range of A/2 if it satisfies 2 cos( A/2)=sqrt(1+sin A)-sqrt(1...

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  12. Find the maximum and minimum of 3sin 2x+4 cos 2x+3

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  13. Prove that -4le5cos theta +3 cos (theta+pi/3)+3le10 for all values of...

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  14. Find the maximum value of1+sin(pi/4+theta)+2cos(pi/4-theta) for all re...

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  15. Find cos(alpha+beta) if tan(alpha/2) and tan (beta/2) are roots of the...

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  16. If sec alpha and cosec alpha are the roots of x^2-px+q=0 then prove...

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  17. IfA+B+C=180^@then prove that sin( A/2)+sin( B/2)+sin( C/2) = 1+4 sin...

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  18. If x+y+z=xyz then prove that (3x-x^3)/(1-3x^2)+(3y-y^3)/(1-3y^2)+(3z-z...

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  19. Simplify the product cos A cos 2A cos2^2A……cos2^(n-1)A

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  20. Prove that the value of underset(r=0)overset10sum cos^3((rpi)/3) is eq...

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