2) Evaluate: sin⁴π/8 + sin⁴3π/8 + sin⁴5π/8 + sin⁴7π/8.
3) Show: sin(2 tan⁻¹1/2)= cos(2tan⁻¹1/3).
4) If (sin⁴x)/a + (cos⁴x)/b = 1/(a + b), show (sin¹⁰x)/a⁴ + (cos¹⁰x)/b⁴ = 1/(a+ b)⁴.
5) Evaluate: 1/(2sin10) - 2 sin 70.
6) If tanx, tany are the roots of x²+ px + q =0, find the value of sin²(x + y) + p sin(x +y) cos(x + y)+ q cos²(x + y).
7) If tan(x + y - z)/tan(x - y + z) = tan z/tan y, show that sin(y - z)= 0 or sin2x + sin2y + sin2z =0.
8) Show that cot70 + 4 cos 70= √3.
9) If cos(x - y)+ cos(y - z)+ cos(z - x)= - 3/2, show that, cos(x - y)= cos(y - z)= cos(z - x)= -1/2.
10) If a, b are two values of x satisfying a tanx + b secx = c, show tan(a+ b)= 2ac/(a²- c²).
11) If (tan(a - b))/tana + sin²c/sin²a = 1, show that tana tanb = tan²z.
12) If tanx = (tan a+ tanb)/(1+ tana tanb), show sin2x= (sin2a + sin2b)/(1+ sin2a sin2b).
2) 3/2 5) 1 6) q
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