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If sin x + sin y + sin z = 0 and cos x ...

If `sin x + sin y + sin z = 0` and `cos x + cos y + cos z = 0` then prove that `cot ((x+y)/2) = cot z` and `cos ((x-y)/2) = pm 1/2`

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A DAS GUPTA-Circular Functions, Identities -Exercise
  1. If sqrt(a + b) tan( theta/2) = sqrt(a -b) tan (phi/2) then prove that ...

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

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

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

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

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

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

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

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

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

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  11. Prove that sin 27^circ = 1/4 (sqrt(5 + sqrt5) - sqrt(3 - sqrt5)).

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  12. Prove that sin 9^circ = 1/4 (sqrt(3 + sqrt5) - sqrt(5 - sqrt5)).

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  13. Prove that tan 20^circ* tan 80^circ = sqrt3 tan 50^circ.

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  14. Prove that (1+cos (pi/9)) (1 + cos 3pi/9) (1+ cos 5pi/9) (1 + cos 7pi...

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  15. Prove that sin 55^circ - sin 19^circ + sin 53^circ - sin 17^circ = co...

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  16. Prove that cos^(4)pi/8+cos^(4)(3pi)/(8)+cos^(4)(5pi)/8+cos^(4)(7pi)/...

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  17. Prove that tan 9^circ - tan 27^circ -tan 63^circ + tan 81^circ = 4.

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  18. Prove that sin^(4)( pi/8)+ sin^(4) ((3pi)/8) + sin^(4) ((5pi)/8) + sin...

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  19. Prove that cos theta* cos 2theta* cos2^(2)theta * cos2^(3)theta x... ...

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  20. Prove that cos pi/15 * cos 2pi/15* cos3pi/15... . . to 7 factors = 1...

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