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If A +B+C = 180^circ, prove that cos A...

If `A +B+C = 180^circ`, prove that `cos A/2+ cos B/2 +cos C/2 = 4cos (pi-A)/4 * cos(pi-B)/4 cos(pi-C)/4`

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A DAS GUPTA-Circular Functions, Identities -Exercise
  1. Prove that in a triangle ABC, sin^(2)A - sin^(2)B + sin^(2)C = 2sin A...

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  2. Prove that in a triangle ABC, sum (cot B+ cotC)/(tan B + tan C) =1.

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  3. If A +B+C = 180^circ, prove that cos A/2+ cos B/2 +cos C/2 = 4cos (p...

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  4. If alpha + beta- gamma= pi, prove that sin^(2)alpha + sin^(2)beta - s...

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  5. If alpha + beta + gamma = 2 theta, prove that cos theta + cos(theta- ...

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  6. If A + B + C = pi, show that cot A + sinA/(sin B sin C) = cot B + sin...

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  7. If A + B + C = 0, prove that sum sin 2A = 2sum sin A * (1 + sum cos A...

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  8. Prove that tan(x - y) + tan(y - z) + tan(z - x) = tan(x - y) *tan(y -...

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  9. If alpha + beta + gamma + delta = 2pi then prove that sum tan alpha =...

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

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

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

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

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

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

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

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

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

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

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

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