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If x + y + z = xyz, prove that x(1 -y^(2...

If `x + y + z = xyz`, prove that `x(1 -y^(2)) (1- z^(2))+ y(1- z^(2))(1- x^(2)) +z(1-x^(2)) (1- y^(2)) = 4xyz`.

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If x+y+z=xzy , prove that : x(1-y^2) (1-z^2) + y(1-z^2) (1-x^2) + z (1-x^2) (1-y^2) = 4xyz .

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If xy + yz + zx = 1 , show that x/(1-x^(2)) +y/(1-y^(2)) + z/(1-z^(2))= 4xyz/((1-x^(2))(1-y^(2)) (1-z^(2)))

If xy + yz + zx = 1 , show that x/(1-x^(2)) +y/(1-y^(2)) + z/(1-z^(2))= (4xyz)/((1-x^(2))(1-y^(2)) (1-z^(2)))

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

If xy+yz+zx=1 show that (x)/(1-x^(2))+(y)/(1-y^(2))+(z)/(1-z^(2))=(4xyz)/((1-x^(2))(1-y^(2))(1-z^(2)))

If x+y+z=xyz then show that (2x)/(1-x^(2))+(2y)/(1-y^(2))+(2z)/(1-z^(2))=(8xyz)/((1-x^(2))(1-y^(2))(1-z^(2)))

If x+y+z=xyz, then value of (x)/(1-x^(2))+(y)/(1-y^(2))+(z)/(1-z^(2))(x)/(1-x^(2))(y)/(1-y^(2))(z)/(1-z^(2))

A DAS GUPTA-Circular Functions, Identities -Exercise
  1. If alpha + beta + gamma + delta = 2pi then prove that sum tan alpha =...

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  2. If cos(beta - gamma) * cos(gamma - alpha)* cos(alpha - beta) + 1 = 0 ...

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

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

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  5. If A + B + C = pi then show that cot theta = cot A + cot B + cot C ⇔ s...

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  6. If theta = pi/7 prove that cos theta* cos 2theta * cos 3theta = 1/8

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  7. If alpha = 2pi/7 prove that tan alpha *tan 2alpha + tan 2alpha* tan 4a...

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  8. If alpha = 2pi/7 prove that sec alpha + sec 2alpha + sec 3alpha = -4.

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  9. Prove that sin pi/14* sin 3pi/14 * sin 5pi/14 = 1/8.

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  10. Show that :sin pi/7 *sin 2pi/7* sin3pi/7 = sqrt7/8

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  11. If u = sec theta + tan theta then tan theta in terms of u is.

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  12. If sin x + cos x = m(ne pm 1) and sec x + cosec x = n then n in terms ...

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  13. If alpha gt 0 such that tan(x + alpha) = tan x for all x in R then the...

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  14. If theta = 5pi/9 the sign of the expression cos theta + sin theta is.

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  15. If 5cos 2t + 12sin 2t = lambda sin(2t -tan^(-1)mu) where lambda, mu ar...

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  16. If cos A = 3/4 then the value of 32sin( A/2)* sin (5A/2) is.

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  17. If sin(theta + 3alpha) = 3sin(alpha - theta) then tan theta in terms o...

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  18. If 0 lt beta lt alpha lt gamma and cos(alpha + beta) = 4/5, sin(alpha...

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  19. If 4nalpha = pi then the numerical value tan alpha* tan 2alpha *tan 3...

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  20. Let sin^(3)x* sin 3x = sum(m=0)^(n) cm cos mx be an identity in x wher...

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