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Prove that cot 142.5^circ = sqrt2 + sqrt...

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

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

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

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

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

Prove that: "tan" 142(1^(@))/(2)=2+sqrt2-sqrt3-sqrt6 .

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sqrt2+ sqrt3+sqrt4+sqrt6 is equal to

Prove that: tan142(1^(@))/(2)=2+sqrt(2)-sqrt(3)-sqrt(6)

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

Prove that, cot 7 1/2 ^@ or tan 82 1/2 ^@ = (sqrt(3)+sqrt(2))(sqrt(2)+1) or sqrt(2)+sqrt(3)+sqrt(4)+sqrt(6)

A DAS GUPTA-Circular Functions, Identities -Exercise
  1. If alpha + beta and alpha - beta are solutions of theta for the equati...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. Prove that sin pi/14* sin 3pi/14* sin 5pi/14........... to 7 factors ...

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  16. If A gt 0, B gt 0 and A + B = pi/3 then find the maximum value of tan...

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  17. Find the minimum value of 9tan^(2)theta + 4cot^(2)theta.

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  18. Show that the maximum and minimum values of sqrt(a^(2)cos^(2)theta + ...

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  19. Find the set of possible values of (tan(x + pi/6))/tan x where x is an...

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  20. Prove that for real x, (tan(x+alpha))/(tan(x-alpha)) where alpha ne pi...

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