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63Trigonometry Show that Cos A + Cos (4π/3 - A) + Cos (4π/3 + A) = 0
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Show that Cos(π/5)Cos(2π/5)Cos(3π/5)Cos(4π/5) = 1/16
Show that Cot(π/20)Cot(3π/20)Cot(5π/20)Cot(7π/20)Cot(9π/20) = 1
Show that Sin(π/5)Sin(2π/5)Sin(3π/5)Sin(4π/5) = 5/16
Show that Cos^2(π/10) + Cos^2 (2π/5) + Cos^2 (3π/5) + Cos^2(9π/10)= 2
Show that Sin^2(π/10) + Sin^2 (2π/5) + Sin^2 (3π/5) + Sin^2(9π/10)= 2
Show that Sin A Sin (60 + A) Sin (60 - A) = 1/4(Sin3A) and hence deduce that Sin20Sin40Sin60Sin80= 3/16
Show that Cos A Cos (60 + A) Cos (60 - A) = 1/4(Cos3A) and hence deduce that Cos(π/9)Cos(2π/9)Cos(3π/9)Cos(4π/9) = 1/16
If 3A is not equal to (2n + 1)π/2 then show that Tan A Tan (60 + A) Tan (60 - A) = Tan 3A and hence deduce that Tan6Tan42Tan66Tan78 = 1
Show that Cos A + Cos (4π/3 - A) + Cos (4π/3 + A) = 0
Show that SinA + Sin(4π/3 + A) - Sin(4π/3 - A) = 0
Show that Cosβ + Cos(2π/3 + β) + Cos(4π/3 + β) = 0
Show that Sinβ + Sin(2π/3 + β) + Sin(4π/3 + β) = 0
Show that Cos^2(β) + Cos^2(2π/3 + β) + Cos^2(2π/3 - β) = 3/2
Show that Sin^2(β) + Sin^2(2π/3 + β) + Sin^2(2π/3 - β) = 3/2
Show that Sin^2(A) + Sin^2(A+B) + 2SinASinBCos(A+B) is independent of A
Show that Cos^2(A-B) + Cos^2(B) - 2Cos(A-B)CosACosB is independent of B
Show that Sin^2(β-π/4) + Sin^2(β+π/12) - Sin^2(β-π/12) = 1/2
Show that Cos^2(β-π/4) + Cos^2(β-π/12) - Cos^2(β+π/12) = 1/2
Show that Sin^2(β) + Sin^2(β+π/3) + Sin^2(β-π/3) = 3/2
Show that Cos^2(β) + Cos^2(β+π/3) + Cos^2(β-π/3) = 3/2
If A, B, C, D are the angles of a cyclic quadrilateral then show that Sin A - Sin C = Sin D - Sin B and Cos A + Cos B + Cos C + Cos D = 0
Show that Cos A Cos 2A Cos 4A Cos 8A = Sin 16A / 16Sin A and hence deduce that Cos (2π/15) Cos (4π/15) Cos (8π/15) Cos (16π/15) = 1/16
If A+B+C = π then show that Sin2A + Sin2B + Sin2C = 4 SinA.SinB.SinC
If A+B+C = π then show that Sin2A + Sin2B - Sin2C = 4 CosA.CosB.SinC
If A+B+C = π then show that Cos2A + Cos2B + Cos2C = -1 - 4 CosA.CosB.CosC
If A+B+C = π then show that Cos2A + Cos2B - Cos2C = 1 - 4 SinA.SinB.CosC
If A+B+C = π then show that SinA + SinB + SinC = 4 Cos (A/2).Cos(B/2).Cos (C/2)
If A+B+C = π then show that SinA + SinB - SinC = 4 Sin (A/2).Sin (B/2).Cos (C/2)
If A+B+C = π then show that CosA + CosB + CosC = 1 + 4 Sin (A/2).Sin (B/2).Sin (C/2)
If A+B+C = π then show that CosA + CosB - CosC = -1 + 4 Cos (A/2).Cos (B/2).Sin (C/2)
If A+B+C = π then show that Cos^2(A) + Cos^2(B) + Cos^2(C) = 1 - 2 Cos A.Cos B.Cos C
If A+B+C = π then show that Cos^2(A) + Cos^2(B) - Cos^2(C) = 1 - 2 Sin A.Sin B.Cos C
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Show that Cot(π/20)Cot(3π/20)Cot(5π/20)Cot(7π/20)Cot(9π/20) = 1
Show that Sin(π/5)Sin(2π/5)Sin(3π/5)Sin(4π/5) = 5/16
Show that Cos^2(π/10) + Cos^2 (2π/5) + Cos^2 (3π/5) + Cos^2(9π/10)= 2
Show that Sin^2(π/10) + Sin^2 (2π/5) + Sin^2 (3π/5) + Sin^2(9π/10)= 2
Show that Sin A Sin (60 + A) Sin (60 - A) = 1/4(Sin3A) and hence deduce that Sin20Sin40Sin60Sin80= 3/16
Show that Cos A Cos (60 + A) Cos (60 - A) = 1/4(Cos3A) and hence deduce that Cos(π/9)Cos(2π/9)Cos(3π/9)Cos(4π/9) = 1/16
If 3A is not equal to (2n + 1)π/2 then show that Tan A Tan (60 + A) Tan (60 - A) = Tan 3A and hence deduce that Tan6Tan42Tan66Tan78 = 1
Show that Cos A + Cos (4π/3 - A) + Cos (4π/3 + A) = 0
Show that SinA + Sin(4π/3 + A) - Sin(4π/3 - A) = 0
Show that Cosβ + Cos(2π/3 + β) + Cos(4π/3 + β) = 0
Show that Sinβ + Sin(2π/3 + β) + Sin(4π/3 + β) = 0
Show that Cos^2(β) + Cos^2(2π/3 + β) + Cos^2(2π/3 - β) = 3/2
Show that Sin^2(β) + Sin^2(2π/3 + β) + Sin^2(2π/3 - β) = 3/2
Show that Sin^2(A) + Sin^2(A+B) + 2SinASinBCos(A+B) is independent of A
Show that Cos^2(A-B) + Cos^2(B) - 2Cos(A-B)CosACosB is independent of B
Show that Sin^2(β-π/4) + Sin^2(β+π/12) - Sin^2(β-π/12) = 1/2
Show that Cos^2(β-π/4) + Cos^2(β-π/12) - Cos^2(β+π/12) = 1/2
Show that Sin^2(β) + Sin^2(β+π/3) + Sin^2(β-π/3) = 3/2
Show that Cos^2(β) + Cos^2(β+π/3) + Cos^2(β-π/3) = 3/2
If A, B, C, D are the angles of a cyclic quadrilateral then show that Sin A - Sin C = Sin D - Sin B and Cos A + Cos B + Cos C + Cos D = 0
Show that Cos A Cos 2A Cos 4A Cos 8A = Sin 16A / 16Sin A and hence deduce that Cos (2π/15) Cos (4π/15) Cos (8π/15) Cos (16π/15) = 1/16
If A+B+C = π then show that Sin2A + Sin2B + Sin2C = 4 SinA.SinB.SinC
If A+B+C = π then show that Sin2A + Sin2B - Sin2C = 4 CosA.CosB.SinC
If A+B+C = π then show that Cos2A + Cos2B + Cos2C = -1 - 4 CosA.CosB.CosC
If A+B+C = π then show that Cos2A + Cos2B - Cos2C = 1 - 4 SinA.SinB.CosC
If A+B+C = π then show that SinA + SinB + SinC = 4 Cos (A/2).Cos(B/2).Cos (C/2)
If A+B+C = π then show that SinA + SinB - SinC = 4 Sin (A/2).Sin (B/2).Cos (C/2)
If A+B+C = π then show that CosA + CosB + CosC = 1 + 4 Sin (A/2).Sin (B/2).Sin (C/2)
If A+B+C = π then show that CosA + CosB - CosC = -1 + 4 Cos (A/2).Cos (B/2).Sin (C/2)
If A+B+C = π then show that Cos^2(A) + Cos^2(B) + Cos^2(C) = 1 - 2 Cos A.Cos B.Cos C
If A+B+C = π then show that Cos^2(A) + Cos^2(B) - Cos^2(C) = 1 - 2 Sin A.Sin B.Cos C
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