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Prove that sin x* sin y*sin(x - y) + si...

Prove that `sin x* sin y*sin(x - y) + sin y *sin z*sin(y- z) + sin z *sin x sin(z - x) + sin(x - y) *sin(y - z)*sin(z -x) = 0`.

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A DAS GUPTA-Circular Functions, Identities -Exercise
  1. If x in (pi, 2pi), prove that ((sqrt(1+cosx))+(sqrt(1-cos x)))/((sqrt(...

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

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  3. Prove that sin x* sin y*sin(x - y) + sin y *sin z*sin(y- z) + sin z ...

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  4. Prove that (3 + cos 4theta) cos 2theta = 4(cos^(8)theta - sin^(8)theta...

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  5. Prove that cos^(2)theta + cos^(2)(alpha + theta) – 2cos alpha *cos th...

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  6. If sin beta = 1/5 sin(2alpha +beta), show that tan(alpha +beta) = 3/2...

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  7. If Tn = sin^(n)theta + cos^(n)theta then prove that (T5 -T3): (T7- T5...

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  8. If f(alpha, beta) = cos^(4)alpha/cos^(2)beta + sin^(4)alpha/sin^(2)bet...

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  9. If cos A = tan B, cos B = tan C and cos C = tan A then show that sin A...

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  10. Prove that cos theta =(cos alpha- cos beta)/(1 -cos alpha*cos beta) ⇔ ...

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  11. If sqrt(a + b) tan = theta/2 = sqrt(a -b) tan phi/2 then prove that a ...

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  12. If sin theta - sin phi = a and cos theta + cos phi = b then prove tha...

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  13. If sin x + sin y + sin z = 0 and cos x + cos y + cos z = 0 then prove...

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  14. If sin alpha + sin beta =p, cos alpha + cos beta = q then find the va...

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  15. If cos(x - y)= -1, show that cos x + cos y = 0 and sin x + sin y = 0.

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  16. If alpha, beta be the solutions of theta for the equation a tan theta...

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  17. If alpha + beta and alpha - beta are solutions of theta for the equati...

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  18. Prove that tan7 1^circ/2 = sqrt6 - sqrt3 + sqrt2 - 2.

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  19. Prove that cot 142.5^circ = sqrt2 + sqrt3 - sqrt4 - sqrt6.

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  20. Prove that sin 23pi/24 = sqrt((2 sqrt2 - sqrt3 -1)/(4 sqrt2))

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