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If sqrt(a + b) tan = theta/2 = sqrt(a -b...

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

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A DAS GUPTA-Circular Functions, Identities -Exercise
  1. If cos A = tan B, cos B = tan C and cos C = tan A then show that sin A...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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