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If A + B + C = pi then show that cot the...

If `A + B + C = pi` then show that `cot theta = cot A + cot B + cot C ⇔ sin(A - theta) * sin(B - theta)* sin(C - theta) = sin3theta`.

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A DAS GUPTA-Circular Functions, Identities -Exercise
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  2. If x + y + z = xyz, prove that (3x -x^(3))/ (1-3x^(2)) + (3y -y^(3))/(...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. If (cos (alpha1- alpha2))/(cos (alpha1+ alpha2)) = (cos (alpha3+ alph...

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  20. If sin x + sin y = a, cos x - cos y = b then the value of tan ((y-x)/2...

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