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If tan^(3) (alpha/2+ pi/4) = tan(beta/2 ...

If `tan^(3) (alpha/2+ pi/4) = tan(beta/2 +pi/4)` then prove that `sin beta = ((3 + sin^(2)alpha) sin alpha) /(1 + 3sin^(2)alpha)`

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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. If tan^(3) (alpha/2+ pi/4) = tan(beta/2 +pi/4) then prove that sin be...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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