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1) A regular hexagon and a regular dodecagon are inscribed in the same circle. If the side of the dodecagon is √3-1, fine the side of the hexagon 2) Fine the value of 1/cos290 + 1/√3sin250 3) Fine the value of cotx + cot60+x + cot120+x 4) If x belongs to π, 3π/2 then find the value of 4cos^2 (π/4 - x/2) + √4sin^4+sin^2 2x 5) If A+B+C = 3π/2, find cos2A+cos2B+cos2C 6) If cos(theta + phi) = mcos(theta - phi) find tan Theta

1) A regular hexagon and a regular dodecagon are inscribed in the same circle. If the side of the dodecagon is √3-1, fine the side of the hexagon
2) Fine the value of 1/cos290 + 1/√3sin250
3) Fine the value of cotx + cot60+x + cot120+x
4) If x belongs to π, 3π/2 then find the value of 4cos^2 (π/4 - x/2) + √4sin^4+sin^2 2x
5) If A+B+C = 3π/2, find cos2A+cos2B+cos2C
6) If cos(theta + phi) = mcos(theta - phi) find tan Theta

Grade:11

1 Answers

Arun
25750 Points
4 years ago
Dear student
 
Please ask only question in one thread.
1)
 

For dodecagon sin(2π/40) = (a/2)/r     so    r = (a/2)/ sin(π/20)

now for hexagon sin(2π/12) = (x/2)/r       so x/2 = r sin(π/6)  =  (a/2) sin(π/6)/ sin(π/20)  

so  x  = (√3-1) (1/2) / ((√5-1)/4)                      here sin(π/20) = (√5-1)/4

or x = 4(√3-1) / 2(√5-1) 

now solve it for further simplification

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