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If cos(beta - gamma) * cos(gamma - alpha...

If `cos(beta - gamma) * cos(gamma - alpha)* cos(alpha - beta) + 1 = 0` then prove that at least one of the angles `beta - gamma, gamma- alpha` and `alpha - beta` is an odd multiple of `pi`.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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