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If alpha, beta are acute angles and cos ...

If `alpha, beta` are acute angles and `cos 2alpha = (3cos2beta -1)/(3-cos2 beta)` prove that `tan alpha : tan beta= sqrt2 :1`.

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A DAS GUPTA-Circular Functions, Identities -Exercise
  1. Prove that sin theta = x + p/x is possible for real x if p le 1/4

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  2. If f(x) = 3(sin x - cos x)^(4) + 6(sin x + cos x)^(2) +4(sin^(6)x + co...

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  3. If alpha, beta are acute angles and cos 2alpha = (3cos2beta -1)/(3-cos...

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  4. If tan theta* tan phi = sqrt((x-y)/(x+y)) prove that (x - y cos 2the...

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  5. If x in (pi, 2pi), prove that ((sqrt(1+cosx))+(sqrt(1-cos x)))/((sqrt(...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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