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If cos A = tan B, cos B = tan C and cos ...

If `cos A = tan B`, `cos B = tan C` and cos `C = tan A` then show that `sin A = sin B = sin C = 2sin 18^circ`.

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A DAS GUPTA-Circular Functions, Identities -Exercise
  1. If Tn = sin^(n)theta + cos^(n)theta then prove that (T5 -T3): (T7- T5...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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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