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If x/(tan(theta+alpha)) = y/(tan(theta+b...

If `x/(tan(theta+alpha)) = y/(tan(theta+beta)) =z/(tan(theta+gamma))`, show that `sum (x+y)/(x-y) sin^(2)(alpha-beta) =0`

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If (x)/(tan(theta-alpha)) = (y)/(tan(theta+beta)) = (z)/(tan(theta+gamma)) then sum(x+y)/(x-y)sin^(2)(alpha-beta) is equal to :

If(tan(theta+alpha))/(a)=(tan(theta+beta))/(b)=(tan(theta+gamma))/(c)(a+b)/(a-b)sin^(2)(alpha-beta)+(b+c)/(b-c)sin^(2)(beta-gamma)+(c+a)/(c-a)sin^(2)(gamma-alpha)=0

If (tan(alpha +beta - gamma))/(tan(alpha -beta + gamma)) = (tan gamma/tan beta) show that sin(beta -gamma) =0 or sin(beta -gamma) =0 , or sin2 alpha +sin2 beta + sin2 gamma =0

If tan theta=(tan alpha+tan beta)/(1+tan alpha tan beta) then show that sin2 theta=(sin2 alpha+sin2 beta)/(1+sin2 alpha sin2 beta)

If sin theta=3sin(theta+2 alpha), then the value of tan(theta+alpha)+2tan alpha is

If alpha + beta + gamma = pi , show that : tan (beta+gamma-alpha) + tan (gamma+alpha-beta) + tan (alpha+beta-gamma) = tan (beta+gamma-alpha) tan (gamma+alpha-beta) tan (alpha+beta-gamma)

If x=cos alpha+i sin alpha,y=cos beta+i sin beta then prove that (x-y)/(x+y)=i(tan)(alpha-beta)/(2)

If (tan(alpha+beta-gamma))/(tan(alpha-beta+gamma))=(tan gamma)/(tan beta),(beta!=gamma) then sin2 alpha+sin2 beta+sin2 gamma=(a)0(b)1(c)2(d)(1)/(2)

If alpha+beta=theta and (tan alpha)/(tan beta)=(x)/(y), prove that sin(alpha-beta)=(x-y)/(x+y)sin theta

A DAS GUPTA-Circular Functions, Identities -Exercise
  1. If x/(tan(theta+alpha)) = y/(tan(theta+beta)) =z/(tan(theta+gamma)), s...

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  2. Eliminate theta between cosec theta -sin theta = m and sec theta - cos...

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  3. If cos alpha + cos 2alpha = p,sin alpha + sin 2alpha = q then eliminat...

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  4. If cos alpha = cos beta*cos phi= cos gamma *cos theta and sin alpha = ...

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  5. Eliminate theta between a = cos(theta - alpha), b = sin(theta - beta) ...

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  6. Eliminating alpha from xcos alpha = y cos(alpha +2pi/3) = zcos (alpha ...

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  7. If cos rx + cos ry = ar, r = 1, 2, 3 then prove that 2a1^(3) + a3 = 3...

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  8. Eliminate theta, phi from sin theta + sin phi = a, cos theta+ cos phi ...

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  9. Eliminatetheta from lambda cos 2theta = cos(theta + alpha) and lambda...

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  10. If f(theta) = 1 + sin [pi/4 + theta] + cos (pi/4 + theta). find the ra...

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  11. Prove that the value of 5 cos theta + 3cos (theta + pi/3) +3 lies bet...

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  12. If f(theta) = 11cos^(2)theta + 15sin theta cos theta - 9sin^(2)theta, ...

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  13. Find the maximum and minimum values of sin^(6)x + cos^(6)x.

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  14. In triangle ABC, B = pi/3 and sin A . sin C = x then find the set of ...

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  15. Prove that the relation sin^(2)theta = (x+y)^(2)/(4xy) is not possib...

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  16. Prove that sin theta = x + p/x is possible for real x if p le 1/4

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  17. If f(x) = 3(sin x - cos x)^(4) + 6(sin x + cos x)^(2) +4(sin^(6)x + co...

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  18. If alpha, beta are acute angles and cos 2alpha = (3cos2beta -1)/(3-cos...

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  19. If tan theta* tan phi = sqrt((x-y)/(x+y)) prove that (x - y cos 2the...

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  20. If x in (pi, 2pi), prove that ((sqrt(1+cosx))+(sqrt(1-cos x)))/((sqrt(...

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  21. Show that cot theta* cot 2theta+ cot 2theta *cot 3theta + 2 = cot thet...

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